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