This list for the bad ones are below, but you only need to pop one "level" of baddy (i.e. Sweet Little Girl or Possessed Little Girl - not both). You can pop them with tomatoes (slingshot, tomatoes, or Tomato Rain), funk-fu blasts, and the singing lady all count, knocking them off the edge of the world or into water doesn't appear to count.
It appears to me, that this all needs to be done in one sitting. I tried it once before, where I did level 1-16 in one sitting and 17 - 25 in another, and it didn't pop. Redid it all at once and it popped (pun intended). So if it didn't work for you and you had saved and reloaded, you may want to try to do it all in one sitting.
Basic Level Baddies (these should be all you need to pop):
Little Devil
Boogie Man
Segway Guard
Construction Worker
Texting Person
Stupid Cupid
Danger Chickens
Sharky
Hungry Caveman
Cow Ghost
Insane Dentist
Mole Thief
Lawn Mower Man
Man In Black
Clipboard Volunteer
Mailbox Monster
Shopping Cart Lady
Inquisitor
Obnoxious Tourist
Yeti With A Pencil
Ice Cream Truck
Snotty Sick Kid
Naked Man In A Box
Brother Marvin & Drone
Selfie Person
Football Player
Internet Troll
Medusa Baby
Brother Floyd & Drone
Rabid Fan Boy
Really Scary Devil - unsure of this one
Sweet Little Girl - popped as soon as I popped her
Evolved forms (I only popped half of them so they didn't seem like part of the achievement):
Crazed Boogie
Riot Guard
Freaky Medusa Baby
Golden Cupid
Evil Red Inquisitor
Zombie Dentist
Ghostly Mower Man - I didn't pop
Barbarian UFO - I didn't pop
Costumed Devil
Deadly Ice Cream Truck - I didn't pop
Possessed Little Girl - I didn't pop