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