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