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