This is the first omake mission you receive after beating the first beat'em up part of the game.
It's simply the exact same level, with a single difference that it will track your time it took you to beat the stage.

Note that the timer doesn't stop at the cutscenes, you need to skip all dialog as soon as possible, and getting distraught or wanting to read the text again might ruin your highscore.

After beating omake mission, you will receive a hidden achievement. This will be true for the next omake missions.

At the start of the mission you will receive Stimulant, Suppresant and a Candy.

It's the exact same deal as stage1 omake, only for second and third action levels of the main story respectively.

You receive the exact same items as in stage1. Beating them will also net you hidden achievements.

This is where it finally gets interesting.

This omake mission will require you to beat all previous omake missions in one playthrough. Dying in the middle of the challenge will have you start over from the very first mission. Progressing through each mission will not replenish your health or special attacks or items so you need to conserve them for important parts of the game.

The items you receive at the beginning of the challenge will be the superior variants of items you got in regular omake missions - Super Stimulant, Super Suppressant and a Deluxe Candy.

I recommend this strategy of beating the arcade mode:

• Instead of running directly into the opponent, try to go below or above the enemy, and then ascent/descent upon him to avoid it's attacks. Always try to grapple an enemy and trash it around by mashing left and right. This way you will deal damage to entire hordes of attackers at once.
  
• When you encounter jumping girls in third part of the game, grapple other enemies and try to damage the jumping girls with the blowback.
  
• Use your special attacks during the second part of the game on the mid-bosses to soften them up. They have very hard attack patterns so it's preferable to avoid the fight at all rather than waste valuable health points. You shouldn't use special attacks at the first part and they will be fairly useless during the third part.
  
• Try to hold up with using Deluxe Candy until you reach third part. If you can't, you should just restart the game and try again.
  
• Save Super Suppressant for the final form of the final boss - her first form is too easy to waste items on.
  
• Use Super Stimulant for whatever boss enemy gives you most problems since it's not too useful for the final battle anyway.

Beating arcade mode will unlock a final omake and will give you a final hidden achievement.

The final omake part is the game OST. The songs are nubered from 0 to 6. Feel free to listen to the game's cacophonic soundtrack. You will not receive any achiement for using this one.