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