Here is the full list of all 45 The Forest achievements. It takes around 50-60 hours to unlock all of the achievements on Windows.
Kill all animal types and display heads
Catch fish with a trap. Alone in Single Player or together in Multiplayer.
Eat an entire family
Grow all plant types
Explore all caves
Eat all mushroom types
Find all missing passengers
Collect all robot pieces
Kill 6 or more fish with a stick of dynamite. Alone in Single Player or together in Multiplayer.
Use the compass
Collect all cassette tapes!
Craft all items
Play through entire game without killing or eating animals. Alone in Single Player or together in Multiplayer.
Set off 20 bombs
Killed downed enemy with rock
Chop up 50 bodies
Craft 10 medicine items
Finish Game
Build a super long wall
Revive 10 co-op players
In Single Player, kill 100 cannibals
Kill a bunny. Alone in Single Player or together in Multiplayer.
Knock down 6 or more trees with 1 explosive. Alone in Single Player or together in Multiplayer.
Kill shark. Alone in Single Player or together in Multiplayer.
Sleep on yacht
Cut down 1000 trees
Cut down 100 trees
Pass 50,000 steps
Eat an enemy
Sleep with another player (group sleep)
Share a weapon in MP
Share a food or drink item in MP
Revive one co-op player
Make and wear stealth armour
Repair a shelter
Survive 1 night
Survive 5 nights
Kill bird with arrow
In Single Player, don't kill any cannibals for more than 10 days in a row