Here is the full list of all 22 Helix Brawl achievements.
Beat Level 1
Beat Level 2
Beat Level 3
Beat Level 4
Beat Level 5
Beat Level 1 without losing more than 50% HP
Beat Level 2 without losing more than 50% HP
Beat Level 3 without losing more than 50% HP
Beat Level 4 without losing more than 50% HP
Stare at the main menu for over 5 minutes straight
Die to an enemy named James
Play the credits 3 times
Defeat 10 enemies
Defeat 20 enemies
Defeat 30 enemies
Defeat 50 enemies
Defeat 4 enemies or more at once with the Bat or Gorilla super attack
Heal to full from a Bat Super
Punch the test tube in Level 1
Die 10 times
Defeat an enemy named Jarred
Stare at the art in Level 4 for 30 seconds