Here is the full list of all 31 Goat Simulator trophies - there are 10 bronze, 15 silver, 5 gold and 1 platinum.
Ride a bike for 60 sec
Find the Sanctum 2 Walker Statue
We are each our own devil, and we make this world our hell
Find all the blocks
Hold your own concert
Get up on the skyscraper without using the elevator
I'm sorry about my goat
Fight the turtle
Why did you step in that? Yuck
Make sure the Hillbilly never drives again
Hit the party with the Boulder of Death
Do no evil
Have 10 gas canisters explode at the same time
Find the Sanctum 1 Walker Statue
Travel to space!
Win the title bout!
Thrash the Goathenge
Become the Queen of GoatVille
Unlock all the Goat Trophies!
Lick the Hanging Glider
Everything the light touches is your kingdom
Bounce 100 times on mattresses within 30 seconds
Sacrifice the 3 Sanctum items
Visit 5 trampolines in one jump, bouncing on each trampoline once
Find all the trophies in Goat Ville!
Finish all manual quests
Score 10 points in Flappy Goat
Go on the catapult with a rider on your back
Lick the rollercoaster with 6 batteries attached
Buy all hats
Find all collectibles on level 2