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