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.
In Single Player, don't kill any cannibals for more than 10 days in a row
Collect all robot pieces
Craft 10 medicine items
Knock down 6 or more trees with 1 explosive. Alone in Single Player or together in Multiplayer.
Chop up 50 bodies
Share a weapon in MP
Use the compass
Finish Game
Sleep on yacht
Set off 20 bombs
Kill shark. Alone in Single Player or together in Multiplayer.
Eat all mushroom types
In Single Player, kill 100 cannibals
Eat an entire family
Collect all cassette tapes!
Eat an enemy
Kill bird with arrow
Survive 5 nights
Kill a bunny. Alone in Single Player or together in Multiplayer.
Cut down 100 trees
Share a food or drink item in MP
Make and wear stealth armour
Revive 10 co-op players
Revive one co-op player
Survive 1 night
Sleep with another player (group sleep)
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.
Explore all caves
Killed downed enemy with rock
Build a super long wall
Kill 6 or more fish with a stick of dynamite. Alone in Single Player or together in Multiplayer.
Find all missing passengers
Pass 50,000 steps
Repair a shelter
Cut down 1000 trees
Catch fish with a trap. Alone in Single Player or together in Multiplayer.