Background
I decided to speedrun this game after having watched Arino from Gamecenter CX playing it. If you're reading these words, chances are that you know what Gamecenter CX is. If you don't, chances are that you will like it. Especially the two Mighty Bomb Jack episodes (one in the recording studio and one in front of a live audience) are well worth watching in my opinion (just be sure to find the ones with subs!). It gives a fairly accurate representation of the complete bullshit this game is. I'd like to develop that last thought a bit more before moving on. I think the gameplay is actually very good. The controls are awesome and Jack has a whole arsenal of different moves (in comparison to many other games from that era) to help him navigate through the levels. It seems that such a good foundation to build on would be a guarantee for a good game. Unfortunately, the developers completely messed it up from there on. The levels are very uninspiring and they all look pretty much the same. There are no fun puzzles to solve and always the same enemies. There are secrets to unlock a better ending (simliar to Solomon's Key), but getting them without a walkthrough and/or a vast amount of save state practice would require crazy dedication. The fact that there are no continues or passwords and that extra lives are pretty hard to come by does not work in favor of this game either. I will however give the game credit for presenting a speedrunner with a few interesting and original challenges.

There is more than meets the eye in Mighty Bomb Jack. In order to document these aspects of the game, I have a created strategy wiki with focus on speedrunning. I will therefore not repeat myself in these comments. The interested reader is asked to go here:
https://kb.speeddemosarchive.com/Mighty_bomb_jack_(nes)

Run comments
I won't go into too much detail here. Mostly point out a few mistakes. If there are faster solutions shown in the speedrun wiki, it's mainly because I wasn't consistent enough at them and decided to trade time for safety.

• PR7 - I missed the exit and lost 0.3 sec. I just mash the jump button after the last bomb has been collected. From experience, it's basically a 50/50 chance whether I manage to enter the exit directly or if I hit the wall first.
• PR8 - Slightly slow in the top left corner. Usually, the mummy walks to the left and not into the wall. If it walks to the left, you need to be careful not descending to fast. Overall a minor time loss though. This is the beginning of some quite interesting enemy manipulation in the next few rooms. Please look in the speedrun wiki for a description of what's going on.
• PR9 - I got a fireball spawn, which is more risky than a bird. With a good fireball pattern, there is however also the possibility to gain a tiny bit of time by being able to jump straight to the exit without hitting the wall first. I had that luck this time.
• PR12 - I had to take a few steps to the right before the last jump to the exit. This horizontal movement could have been done during drop down instead. A few frames lost.
• PR13 - The room solution here looks treacherously simple, but it's actually the result of some fairly technical enemy manipulation. Both in this room and in the previous rooms. This room is normally the hardest room (by far) in the game. Ask Arino if you don't believe me...
• PR14 - Having passed the ordeal of room 13, I used a rather conservative approach in this room. It would of course have been faster to collect the six last bombs in one single jump, but it's also a bit risky. If anyone wants to improve on this run, I recommend including the faster method. It would have saved around 0.5 sec, which is pretty significant at this point.
• PR15 - Just like in PR14, I played this room conservatively. If you're too fast, there is a very real possibility of jumping into the mummy before collecting the three last bombs. I deliberately took it a bit slow in order to prevent that. In hindsight, I could have pressed on a bit harder. Minor time loss though.
• PR16 - There is a slightly faster (~0.3 sec) room solution shown in the speedrun wiki, but I chose this room solution for the sake of consistency.
• Stage 17 - Together with the missed exit in PR7, the biggest execution mistake of the run came here. In the right room, I fell down on top of the chest instead of down to the floor. Compared to other runs I've had, it was a time loss of roughly 0.3 sec, but it looks a bit sloppy.

Final thoughts
When I started playing this game, my goal was to get close to the fastest reported time I could find, rta-time of 7:25 (no video and I also suspect it was played on emulator and with the help of autofire). That time was for the Japanese version, which has a few seconds of disadvantage compared with the US version. It didn't take long to realize that I had routes that would actually give a comparable time. More attempts, more testing and a better and better understanding of the game allowed me to continue to chop off second after second until sub-7 was finally within reach. The last piece that fell into place was how to get through room 13 (before that, it was basically a brick wall). With the route in place, I set my goal to 6:56-6:57. This run was a 6:57, but could have been a high 6:56 with cleaner execution.
By comparing the level completion times in this run with some of my other attempts, it's clear that even a solved room with no particular mistakes can be 10-15 frames off the best attempts. By dedicating more time to this game, I'm sure it would be possible to eventually lower the average completion times that would add up to another second or two over the course of the run. Before heading into some of the room solutions seen in the tases, there are also a couple of mine that I admit are a bit conservative. Having another pair of eyes coming up with ideas could of course also bring up some improvement. So there is still potential left in this category. However, I think this is how far I'm prepared to go for now with this category. I plan to look into the best ending as my next step.

Background
I started working on a best ending run once I had recorded my normal ending run. At first I wanted to do a no death, no warp run to differentiate it from the normal ending run and show off as much as possible of the game. However, I soon realized that all the levels are just like others. There is not much in terms of "level themes" (fire, ice etc) to make the game interesting to look at. The enemies are the same from level 1 until the last level. There are no new obstacles, no cool items to collect etc. The difficulty stays the same throughout the game. It looks like the developers have just more or less randomly scattered chests and obstacles and then rolled a die to decide which room should go where... I'm exaggerating a bit, but the design is just really uninspired imo. I then decided to just go for the fastest solution (with deaths and warps), even though a good portion of the run is then pretty much identical to the normal ending run.

There is more than meets the eye in Mighty Bomb Jack. In order to document these aspects of the game, I have a created strategy wiki with focus on speedrunning. I will therefore not repeat myself in these comments. The interested reader is asked to go here:
https://kb.speeddemosarchive.com/Mighty_bomb_jack_(nes)
For increased viewing pleasure, I recommend to at least check out the game map:
http://www.vgmaps.com/Atlas/NES/MightyBombJack-Pyramid.png
The path taken in this speedrun is: 1-1->Palace room 1->2->3->4->5->6->7-1->7-2->7-4->7-5->7-7->7-8->7-9->7-10->7-9->10-1->10->11->12-1->12-2->12-3->12-4->12-10->12-13->12-15->12-16->12-17->12-18->12-19->12-20->12-19->12-18->12-22->12-23->12-26->12-27->12-28->12-29->12-30->[death abuse]->12-1->12->13->14->15->16-1->[death abuse]->16-1->16-2->16->17-1->17-2->17-1->K->Q->P->B. Easy, right? :-)

Run comments
I won't go into too much detail here. Mostly point out a few mistakes. If there are faster solutions shown in the speedrun wiki, it's mainly because I wasn't consistent enough at them and decided to trade time for safety.

• 13 - Everything had gone surprisingly well up to this point. Unfortunately, I jumped slightly too early in the lower right corner and got an unfavorable spawn. Ideally, there will be two fireballs and two bats. Here I got one bird instead of a bat. That requires a small detour, which costs ~1 second. This room doesn't look hard when seeing it played like this, so I know you will have a hard time believing me saying that it's such a pain in the ... I therefore don't have too many regrets about the lost time.
• 14 - Small mistake at the beginning. Maybe the nerves kicking in (not many good runs get past palace room 13)? It is actually pretty difficult to pick up that bomb on the fly though. Maybe half a second lost.
• 17-1 (1st visit) - I missed the first double jump when destroying the blocks above the sphinx. It looks ugly, but is unfortunately something that happens at least once in most runs. Around half a second lost.
• K, Q, P and B - Several minor mistakes in the end gauntlet and also some cautious playing. I absolutely wanted to avoid bumping the head into any of the platforms when going for the exit (easily done). I think these rooms could be done around 2 seconds faster with more aggressive playing and less mistakes.

Final thoughts
Once I had the route pinned down and started to get a few finished runs, I set a goal time of 12m05s, with the hope of maybe even getting a 12m04s with some luck (I knew it could be even faster than that, but I didn't have the ambition to continue pushing down the time forever). I'm therefore a bit ambiguous about the 12m06s. I feel there is maybe one or two mistakes too many, but at the same time I don't feel like grinding out this game for one or two seconds. I hope it was still an enjoyable watch!