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