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.
In Single Player, don't kill any cannibals for more than 10 days in a row
Make and wear stealth armour
Use the compass
Kill a bunny. Alone in Single Player or together in Multiplayer.
Survive 5 nights
Kill bird with arrow
Survive 1 night
Eat an enemy
Eat an entire family
Share a food or drink item in MP
Share a weapon in MP
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
Sleep on yacht
Explore all caves
Revive one co-op player
Revive 10 co-op players
Sleep with another player (group sleep)
Killed downed enemy with rock
Build a super long wall
Chop up 50 bodies
Kill 6 or more fish with a stick of dynamite. Alone in Single Player or together in Multiplayer.
Finish Game
In Single Player, kill 100 cannibals
Find all missing passengers
Kill shark. Alone in Single Player or together in Multiplayer.
Collect all cassette tapes!
Eat all mushroom types
Pass 50,000 steps
Set off 20 bombs
Repair a shelter
Collect all robot pieces
Cut down 100 trees
Cut down 1000 trees
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.