Completed with Max at Mania difficulty with no lives lost. I also maxed out the score, which was nice.

Phil You have being hitted in you run. Is it for saving time? For me it seems not. I'm waiting your answer.

All the hits taken were weak, non-knockdown attacks. When playing as Max, it tends to take longer to prevent or avoid these than it does to just ignore them (he's slow - go figure).
Also note that at Mania difficulty, if an enemy is in range then they WILL attack. You can't abuse savestates to get them to not do so.

There are also some occasions when I purposefully got hit to save time:
Double Specials
If you get hit at the start of a special, you can instantly release another one. I occasionally did this to take out enemies on both sides at once with a Thunder Tackle in each direction.
Move Interruption
If you get hit during the animation of a move, you can use it again as soon as the recoil wears off. The third attack in Max's combo (roundhouse) can hit up to 5 times. If someone is stood behind you when you use it, then they will punch you after a few hits. After recovering from the punch, you can use another roundhouse, hitting the enemy behind you once, and doing another load of damage to whoever is in front of you. It will again be interrupted by the guy behind you, and you can use another roundhouse... and another... and another... I used this technique to kill Jet (2nd boss) ridiculously quickly.

Bisqwit: reopened

Bisqwit: I can't say whether this movie is good or bad, but since it has been requested, I'll process it now.

Bisqwit: Done.