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