Here is the full list of all 56 Home Sheep Home: Farmageddon Party Edition trophies - there are 48 bronze, 5 silver, 2 gold and 1 platinum.
Unlock every other trophy
Complete Underground level 1
Complete Underground level 3
Complete Underground level 10
Complete Underground level 15
Complete London level 1
Complete London level 5
Complete London level 10
Complete London level 15
Complete Space level 1
Complete Space level 5
Complete Space level 10
Complete Space level 15
Complete Graze School training
Complete Further Ed-ewe-cation training
Complete Ewe-niversity training
Complete any one bonus level
Complete any five bonus levels
Complete any ten bonus levels
Complete all bonus levels
Complete all episodes
Find a giant cake
Toast Shaun on a rocket in the last space level
Complete London level 1 with the luggage on board
Smash 5 speed cameras in a row in London level 3
Get a photo of every sheep in London level 3
Complete London level 5 with all chimneys intact
Use just 2 'chutes to survive the mineshaft fall
Complete Underground level 5 without using any TNT
Complete Underground level 6 with TNT to spare
Solve Space level 4 with only two teleport swaps
Change sheep selection just once in Space level 14
Surf the camper van home in London level 15
Cross Big Ben's clockface without moving the hands
Get all three sheep flying together using the chimney
Don't touch the football in Space level 6
Complete any level with a three star rating
Complete five levels with three star ratings
Complete thirty levels with three star ratings
Complete all story levels with three star ratings
Beat the developers' time on any one level
Find two missing woolly socks
Find twelve socks, one for each hoof!
Find 24 cosy socks
Find fifty socks, enough for any sheep
Find seventy five socks, a lifetime's supply
Find every woolly sock in the game
Find a hidden cake
Unlock a bonus level by finding a hidden joypad
Find every hidden cake
Find 15 joypads
Collect everything possible from every level!
Complete Farm level 1
Complete Farm level 3
Complete Farm level 10
Complete Farm level 15