Batman for the Arcade is a licensed action platformer, based on the 1989 Batman movie, in which you take Batman down his daily midnight stroll through Gotham, beating up thugs, and the Joker, and some guy that falls into a pool of acid..

If you press buttons 1 or 2 mid jump at specific frames, Batman's jump will be reduced, this is beneficial since walking is faster than jumping.
The button to press depends on the type of jump, if its the standard one, 1 should be pressed, which is the attack button, but if the jump is the drop kick, 2 should be pressed.
The other jump kick can't be reduced.

When attacking, in any way, the animation can be cancelled early by looking back and not holding any directions in specific frames.

RNG depends on input, so if you hold L+R for 1 or 2 frames, for example, RNG can be maniped without losing any time.

The kind of jump you do depends on how close you are to an enemy, so many times its beneficial to turn around just before jumping to do a normal jump to jump over an enemy, instead of doing a jump attack, since that would push the enemy away and would have to be attacked again to clear him.

In the first stage there's supposed to be enemies, but all of their spawns are RNG so can be maniped, this won't be possible in the next stages unfortunately.

In the stage after the joker cars section, Batman goes backwards for a bit before going forwards again, that's because the screen scroll is locked until a certain point in the level.

Batman's health comes in threes, so if you take three damage and lose one of the Batman icons, Batman dies, this is not the case in the autoscroller sections, where you can only die if you lose all your health, which is why one damage is taken in the helicopter section, so more damage can be taken in the last stage.

In the last stage, it's impossible to jump over Joker, so you have to either push him enough that he falls into one of the holes, or deal enough damage.