I decided to stick with Jecy's rule number 1 - do not take any damage. By having it this way the two runs are more comparable, and from what I saw there's only one scenario in the whole game where taking damage can save time - beginning of level 4-3, perhaps also one on level 2-3 but I didn't test that since taking damage was never an option.
Also worth to mention is that the undo count shown here is about twice as low as the reality would tell, since I competed with myself on at most four moviefiles at the same time and then submitted the one with most rerecords.
Level 1-1
I'm pretty sure that this level is perfect (strong words!) if not a suitable glitch is discovered. There's no frame of lag at all, the jumps are always as high as possible and the number of jumps are absolutely as small as possible.
Level 1-2
From the start to the upper left corner, no frame is gained. Then at the scenario when I'm jumping up the platforms I manages to reduce 7 frame of lag by jumping backwards. 1 frame of route was also gained there.
First boss, HP = 17
I kill the boos with the weapons (in order) 3-way, batarang, batarang, 3-way, fists. I also took advantage of a glitch/trick, don't know where it belongs, that works in the way that when you hit the boss, you don't push him back but in the same direction as Batman faces. By doing it this way I killed the boss 11 frames faster but I just gained 10 on the whole boss cause of a stupid counter rule.
Level 2-1
Improvements came from punching in the air after a wall jump to make Batman stop in the air faster. Due to this I had to lose 5-6 frames on the first flame thrower.
Level 2-2
Frames gained due to some better wall jumps.
Level 2-3
The noteable things in this level is that I instead of jumping over the enemy on the conveyor belt I puch it which is faster. I'm quite surprised this was overlooked. I felt that I could have gained one extra frame on this level if I had worked a few more hours but since the boss had a counter rule I would lose that in either case, hope I'm excused.
Second boss, each component has 17 HP
Due to a global counter that that controlls the shots of the components at the bottom I manage to kill in a little more efficient way.
Level 3-1
Those jumping creatures are a pain their jumping depends on the same global counter as well, and in one place I had to stop for 2 frames - there was simply nothing else to do - life's unfair.
Level 3-2
Here the jumping creatures where nicer which this level very easy to go through. Gained 1 frame, probably due to lag reduction.
Level 3-3
The 5 frames was all gained due to lag reduction. I think Jecy's wall jumping already was perfect.
Third boss, HP = 65
Here I got the biggest improvement in the whole run. Basically I killed the boss before his third jump while Jecy killed him when he almost had landed it. I have to say this fight looks really simple, but I can tell it's many absolutely frame precise movements that lead to this improvement.
Level 4-1
The lag level - oh yeah! A bad jumping creature at the beginning forced me to shoot an extra 3-way at him which ofcourse created lag, if you don't kill him you'll soon face a mega lag. I had however been able to regain every single one of the lost frames when the level was over.
Level 4-2
Most improvements here was because of a different way of handling the scenario with the third flame thrower.
Level 4-3
You'll maybe notice that I'm playing a little suboptimal at the beginning of the level, this is becase I'm waiting for the electricity to disappear. The lost frames came from various places with where affected by the earlier mentioned counter.
Fourth boss, 65 HP each - when one is killed the other get 17
Once I started hitting the left square, I didn't leave it alone very much:)
Level 5-1
Not surprisingly the most improvement on this level comes from the very laggy situation at the lower right corner. By killing one of the blue enemies I get much less lag when I had jumped to the second floor.
Fifth boss(Fire Bug), HP = 97
Main task is to get inside him as fast as possible, the time gained came from more continious punching.
Six boss(Joker), HP = 161
Undoubtly the easiest boss to TAS, improvents from doing one less jump and better planing of ending the input.