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