Mini edit:
This run was made 2 months before the PC Steam announcement which has new content including Speed Run mode which disables Prevasion and ends on the true final chapter thanks to Broken Necklace as one of the items to trigger it. It also turns out that Dash Jumping is a tad faster but you can make a mistake and lose time if you jump before dashing.

ARMED BLUE LIGHTNING SPHERE.

This run uses the overall in-game time(r) which keeps on counting even during the post-credits save screen. It functions a little different than the Stage IL timer where it freezes during Special Skill/Desperation attacks, because of this some of the Stage ILs can be cut down a bit by abusing checkpoint reloads to refill Special Skills but it will make the overall in-game time much longer.

Tricks used in the run:

Anthem/Song of Diva:

This is only used in Merak to enter the secret wormhole and skip a chunk of section one. Normally it requires a double jump upgrade but that requires material drop RNG after completing stages, buying the upgrade and then equipping it. Instead of doing that, I do a death abuse revival that works ~90% of the time.

Reload checkpoint to refill Special Skill

Like I said earlier, this is only used in two stages because it saves a good amount of time. This is used in Streak right before Merak round two and Stratosphere right before Copen round two.

Mashing:

It looks like mashing the fire button is faster than Cerberus's default rapid fire.
For dashing, it's recommended to mash the dash button to abuse the mini-boosts at the start of each dash.

Buffered inputs:

When Gunvolt enters a trap room with a few enemies and a red alarm, you can hold certain inputs to make Gunvolt move/jump/fire as soon as he regains control.

Boss's base defence mechanic:

An unique feature to this game, depending on the boss's actions his/her defence may go up or down. Some bosses may troll the player by abusing attacks that increases their defence making the fight a little longer.
Check out Sairaan's awesome pastebin link below for details:

http://pastebin.com/MjfBV5BX

Upgrades used in this run:

I only use the default perks the game has given to me, buying new upgrade takes too much time and more offensive skills like Spark Calibur requires farming experience points to Level 13, which takes too much time and the time gained by using Spark Calibur isn't worth it.

Bolts used in this run:

Cerberus: Your default gun.
+ Enables rapid fire by holding down the button
- Can tag up to three times.

Three times is pretty bad because there is a boss that can save significant amount of time but requires more than three tags.

Naga: Obtained after defeating one boss.
+ Charged shots goes through walls
+ Can tag up to five times
- Requires mashing because it cannot rapid fire.

I use this bolt at the start of Elise because charged shots allows me to hit far light switches regardless of any obstacle and it can tag up to five times which is very useful against Elise.

Orochi: Obtained after defeating seven bosses.
+ Auto firing bot that can cover the air or the ground.
+ Can tag up to eight times.
- Loses a bit of rapid firing if shot from a distance (three bolts from Gunvolt, five bolts from the bot).

This bolt allows me to level three tag both Elise bodies during the refight.
The bot auto fires covers one half of the screen. Usually the upper or lower half. If Gunvolt initially shot a bolt from the ground then the bot covers the upper half, if Gunvolt initially shot a bolt from the air then the bot covers the lower half.

Stage comments:

Intro:

The early part is basic stuff, the sub bosses. I only use Lightning Sphere against the face because it has a lot more HP than the power supply weak spot. The power supply has way less HP and it is actually faster to use bolts + flashfield.

before Merak:

After mashing the START button, I go to menu and Talk to Joule. This basically increases my chances of getting a powerup revival used in the stage coming right up.

Merak:

Drained my HP to zero and got revived by Lumen's Anthem, in this form. Gunvolt has infinite electricity, can perform infinite air jumps and infinite air dash. The jumps are used to enter the secret wormhole to skip a chunk of section one and quick climb in section two. The infinite jump also helps me kill Merak quicker at point blank range with flashfield + bolts. This boss only increases his defences during his desperation move, so there isn't any bad attack RNG that makes the fight go a bit longer.

Carrera:

The gimmick in this stage is magnetism and it used to be one of the tougher platforming stages. The boss fight itself was a bit unlucky as during phase two Carrera decided to charge up a projectile that increases his defences. I only lose ~4-5 seconds compared to a lucky fight. He is a minor RNG offender as the rest of the fight is predictable.

Elise:

This stage is chosen as stage 3 to take advantage of Naga. Also dark rooms... arrgh.
The only spot I have a hard time mastering the layout is the start of section two. There's so much stuff to remember when going through that part.

The boss fight itself is pretty standard stuff, technically you could try a level three tag an Elise body during phase three but you also need to level three tag the other body to make sure they both die instantly. You could be lucky and kill one by one IF they are busy doing a lengthy attack like petrify beams, swinging from pole to pole or a combo attack.
Their defences stay the same throughout the fight, you just need good RNG to deal with in phase 3 if both of their HP are not equal.

Zonda:

Section one is pretty standard stuff, section two's moving platforms runs in a global timer. This means the small mistake right before the upside down section made no time loss in the run at all. The final part of section two has a pretty tough jump to get across and flashfield was on a bit too long so Gunvolt flinched and had to recover for loss time.

Protoman, err I mean Copen steals the show. Armed with a pistol and a shield, his defences are below average but he also has an ability to use skills from the Sumeragi. Two of the six increases his defences, sadly he did use a skill that increases his defences. Fortunately he did that after his pistol shooting mode so his HP phase bar was at around 30%.

Stratos:

After a few tough platforming stages, this one is actually a little easier.
A few of my past attempts I lost a bit of time because my EP meter was at overheat right before destroying a mandatory vine, to make sure that did not happen, I either:

A) Jump over a few enemies
B) Did a instant refill by pressing down twice.

The boss fight itself was ok, not perfect. The lightning sphere usage is pretty precise.
Phase one sphere usage only dealt 50% and not 75% but this can be a good thing because it allows me to use Lightning sphere during the start of phase two and deal 75% right away. Phase 3 has a time saver that is tough to do without Orochi, you need to do a bit of bolt/flash field damage and use Lightning sphere just before/after Stratos crosses over the middle during his leap. Then when he disappears and re-appears to the middle, you need to quickly shoot enough bolts and flashfield damage to skip the DESTINY FANG cutscene. I was just off by a few HP in the original fight but I did get the skip to work in the refight later on in the run.

Viper:

Section one is usually the my weaker part of the platforming stages, there's so many different obstacle combinations to memorise and flash field management to hover over and land on higher obstacles sooner.
The sub boss fight itself is luck based when it attaches to the ceiling, it either does
A) Charges in
B) Opens up and drop some bombs.
The sub boss did option A and I had to use a Lightning sphere to quickly finish it off once it when through Gunvolt.

Section two I have an easier time memorising as the upcoming obstacles are less varied. There is small time saver I didn't get which is to skip the black block but it runs in a global timer and the execution room of error is pretty small. To be honest that time loss is nothing compared to bad boss luck RNG.

The boss fight itself is actually pretty tough. Even during phase one Viper is not 100% predictable as after his series of shots he either does one or two slides and if you make a bad read, you'll take damage which will lead to problems during phase three. Right after phase two, after I hear Viper's quote, I use Lightning sphere right before his desperation attack. The first usage deals three "chunks" of damage which what I wanted and because my attack is used before Viper's Sunshine Nova, the cool down meter is filled up to the top right before Viper reaches to the top. His defences is the same throughout the fight but RNG difference is phase two where the more time Viper stays on the ground, the more bolts I can fire and deal extra damage.

Jota:

The platforming sections are easier than Viper's thanks to jump pads, I mean BOOST RINGS. The boss fight itself is notably RNG dependent, the difference between a good fight and a bad fight is around fifteen to twenty seconds. Phase one is done in two cycles and phase two is done in one cycle.

Phase one's spike laser placements is preferred because Jota's defences are lower than usual and a well placed Lighting Sphere can deal major damage, his other attack where he uses his spikes as drills actually increases his defence.

Phase two was perfect RNG, he uses charged laser attacks which
A) lower his defences
B) stays in one position long enough to take 75% damage from Lighting sphere and the remaining 25% from flashfield.

Phase three was perfect because, he spawns immediately to the ground and his HP is low enough to die from a Lightning sphere.

Final four stages:

Hostage:

Shortest stage in the game, use Lighting sphere first to deal 75% damage to the face, finish off with flashfield. The power supply weakspot has more HP and requires a Special Skill like Lightning sphere to destroy it in one cycle.

Streak:

Section one requires less jumping because it slows Gunvolt down but at the same time, taking too much EP damage means I have to jump over some enemies or Gunvolt takes real damage. Section two is quite the opposite where dash jumping is notably faster than dashing thank to the wind. The sub boss luck is decent as none of the machines jumped to the left (and possibly jump back to the right).

Merak round two is just like round one except there's two side pits and Gunvolt cannot use infinite flashfield/air hops as he wasn't revived by Lumen.

Stratosphere:

Basically a boss rush with all of the other characters except Carrera.

Stratos round two: No major screwups on my half, could have save a bit of time if he did different attacks right after each Lightning sphere.

Jota round two:
Phase one and two used the same patterns, done in two cycles per phase. I would have lost more time if:
Jota did spear to drill attacks two times in a row (higher defence),
During phase two, each spear takes a turn to fire a laser (wait a bit longer before Jota spawns).
Phase three was pretty fortunate as I can use a Lighting sphere right after Jota's Desperation attack and the attack he used was the best one for speed running.

Viper round two:
Phase two was pretty good, Viper only used his aerial attacks during the last 25% of his phase two HP bar. Phase three is a bit easier thanks to Orochi's auto firing bot tagging Viper during his Desperation attack, I used a Lighting sphere to deal the last 30% of his phase three HP bar.

Elise round two:
Unlike the previous round, this one is significantly harder thanks to a third member who is immortal to Gunvolt's attacks. Fortunately, there is a way to avoid the special kunai attacks by standing next to the middle pole. I gained enough Kudos to trigger a special background music for a split second proves how easy this boss fight can be sometimes. After the intentional resurrection, near the last 10% I did stop attacking for a bit to make sure my EP meter is full and the two bodies were attacking to increase my room of "error" if one did survive for too long.

Copen round two:
Copen gained a few improvements in this fight, his defences are up slightly but is still a tad weaker than a boss's average bulk. He was a bit of a troll when it came to Sumeragi skill choices because he used the same weapon which also increases his bulk. Fortunately, his phase HP bar was pretty low so I can end his bad attack pretty soon.
Phase three has no RNG, he basically uses his Desperation Attack which is apparently based on Zonda and I use my Lightning Sphere when the HP bar is roughly between the B and O from "BOSS"

Idolatry:

The platforming section is pretty basic, the most annoying way to lose time is when you are somehow not dash jumping despite mashing the L button...

Nova:

He isn't too bad because none of his moves increases his defences and his base defence is pretty low. He is also unique along with Nova fusion where he does not gain invincibility after removing a phase HP bar. During phase two, right after his series of purple projectiles, I remove the barrier and use Lightning sphere to take away 75% of a phase bar. By doing that, he uses his Desperation Attack and my cooldown will be filled up and I can use another Lightning sphere right afterwards.
If you use Lighting sphere before removing Nova's barrier then he only takes two "chunks" and only deals 50% instead of 75%.

Nova Fusion:

This boss is annoying in a speed run, probably in the same league as Mega Man X2/Mega Man 9 in terms of RNG trolling. There's two attacks where he intentionally removes a "weak spot" machine and keeps his barrier intact. Sometimes in the fight you deal with these attacks 3 to 4 times, sometimes none. This fight only had one bad attack and it happened during phase three which is pretty good. If only he did it a few seconds later where a Lightning sphere is enough to be in kill range. Oh did I mention that the defence stat is pretty unique where it is equivalent to WEAK when you use flashfield lightning and when you use a Special Skill like Lightning sphere or Spark Calibur the defence is equivalent to RESIST where it doesn't take much damage and it's actually faster to use normal attacks thanks to higher damage per second.
Trust me, this fight alone can be as bad as an unlucky Jota fight.

49:13 is a pretty good start, there's a few parts where I can shave off a few seconds but the real challenge is trying to get a good executed run along with good boss luck RNG. I did have a few bad luck moments but none of the fights were ~20 seconds slower than best possible outcome.

I'll be more motivated to get a faster time in this category when a Loopy 3DS capture card is out for the new3DS (XL) model where it takes advantage on both faster loading screens and quick bolt switching by pressing ZL/ZR. The reason why I am not getting one from Kasukity is because: not only it lacks built-in AVI recordings but they are more prone to malfunction due to modifications being quickly made.