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