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