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