Bronze

Puzzle me this!
Unlock Puzzle mode

Feats of Constipation
Unlock Challenge mode

Crunchicidal Maniac
Pop a chain that is 15 critters long

Wilhelm Von Puzzleworth
Complete 25 Puzzle levels

Last Man Digesting
Survive to level 9 in Survival mode

Smart Mouth
Complete a puzzle level with moves remaining

Feeding Frenzy
Unlock Survival mode

Circle of Life
Complete 10 Food Chains in a single level

Beverage and Fries
Complete 6 Combos in a single level

Smirk Wiper
Win an online Versus match

Veteran Food Eater
Reach experience level 5 in online Versus mode

Silver

World's Greatest Dad!
Complete 35 Adventure levels while also feeding Smalls to completion

Challenge Taker
Complete Challenge mode

Gold

King of the Jungle
Complete both Adventure mode and Puzzle mode

Source: http://crittercrunch.com/?p=303

Some brilliant trophies here, and you can see the images as well in the link above. Enjoy!