THE MASK PRISON BOSS SCIENCE

Normally Gun does 32 damage.
Double hit Gun does 62 damage.

Getting one double hit will make it so you won't need to punch the boss a billion times.

You get a double hit by hitting the boss 1 frame before he hits you with his swing attack.

But note that his swing attack has a two part hitbox, where the first part is a little closer to him and it comes out 1 frame earlier than the second part. You can only get the double hit with this first part of the hitbox. In practice this doesn't matter for getting the double hit at the first gun attack of the fight, but this is why you see the TAS walk towards the boss after the first double hit instead of standing still.

This also means that if you stand still after the initial double hit, not every gun shot can be a double hit because your attacks will push him back.


If you're doing Gun > Horn > Gun > Horn repeat...

The first Gun will have a chance of being a double hit. This one is the most likely to accidently become a double hit because even if you're quick you naturally hit him very late anyway.

The second Gun can be a double hit, but you'll need to actually delay/time the gun shot because he takes half a second to walk towards you. So this is more like a jumproll, and not worth going for.

The third Gun can also unintentionally become a double hit, for the same reason as the first double hit (you naturally hit him late anyway). Although if you're going for this double hit, you should actually time the Gun attack instead of mashing, because mashing could buffer it.
Note that this and all subsequent notes assume that you didn't wait and go for the second double hit, but instead did the previous gun attacks quickly like normal.

The Fourth Gun can only become a double hit if you walk forward a bit beforehand.

The Fifth Gun can still be a double hit if you stayed still instead of walking forward at the fourth gun, but you'll need to time it a half second afterwards much like the second double hit. If you walked forward at the fourth double hit, then you'll need to walk forward here again to make this one possible.


TL;DR:
The First and Third double hits are frame perfect, but they can happen accidently/naturally, and are the ones you want to go for if you're desperate to save the time. Just intentionally time the first hit a bit later, and/or time the third hit instead of mashing.

Although with that being said, there is some RNG in the fight. Sometimes the boss wont always attack quickly at the third hit, so even if you time it perfectly there, you may not have a chance to get this double hit. Regardless going for the double hit at the first hit, and if you miss that, the third hit, is still the best strategy in this fight.

Oh, and it doesn't look like double hit exists with the horn.