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