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