Neighborhorde

There are 40 and they appear at random throughout the game. This will take a few runs and even if you don't complete the run to the final level, the powers you select count. Listed below I believe are the 40 you will need to earn this achievement:

Get to the Choppa
Wake up
Packin
Magnetic
Hot Feet
Next
Big Heart
Ice Slicer
BFFS
Leeroy
Gas Soaked
Chest Bump
Pain is Gain
Recycler
Beat the Heat
Blinky
Summer Lovin
Slippy Slide
Explosive Recall
Beauty Sleep
B-day
Stop Drop and Roll
Picky
Night Light
Ring of Fire
Spoiled
Double Dash
High Fever
Ring of Ice
C3llPhn3z
Fearless
Burrito Dinner
Toy Love
Fishy
Pushy
Super Sonic
Rude Awakening
Pitcher
Rambo
Surprise Party

Happy Hunting!