Here is the full list of all 38 The Forest trophies - there are 22 bronze, 11 silver, 4 gold and 1 platinum.
In a Single Player game, destroy 6 or more trees with 1 explosive
Revive 10 co-op players
Craft 10 medicine items
Chop up 50 bodies
Eat an entire family
Finish Game
Drink from coffee machine
Buy a soda and candy from vending machine
Share a weapon in MP
Killed downed enemy with rock
Be in a game when 6 or more fish are killed with a stick of dynamite
Make and wear stealth armour
In a Single Player game, kill a bird with an arrow
Share a food or drink item in MP
Use the compass
Place a blueprint for a super long wall
In a Single Player game, repair a hunting shelter
Build a gazebo in a Single Player game
Catch a fish with a spear
Sleep on yacht
Sleep with another player (group sleep)
In a Single Player game, kill a bunny
Unlock all trophies
Plant all 3 seed types
Collect all cassette tapes!
In a Single Player game, set off the sprinklers
Cut down 1000 trees
Collect all robot pieces
Kill shark in Single Player
Eat all mushroom types
Drink water from cooler that has the lawyer head in it
Survive 100 days without finding your son
Pass 50,000 steps
Play through entire game without killing or eating animals
Craft all items
Explore all caves
Kill all animal types and display heads
Find all missing passengers