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
Pass 50,000 steps
Cut down 1000 trees
Play through entire game without killing or eating animals. Alone in Single Player or together in Multiplayer.
Build a super long wall
Explore all caves
Kill all animal types and display heads
Eat all mushroom types
Finish Game
Killed downed enemy with rock
Catch fish with a trap. Alone in Single Player or together in Multiplayer.
Craft all items
Kill 6 or more fish with a stick of dynamite. Alone in Single Player or together in Multiplayer.
Find all missing passengers
Set off 20 bombs
Collect all robot pieces
Grow all plant types
Kill shark. Alone in Single Player or together in Multiplayer.
Collect all cassette tapes!
Eat an entire family
Repair a shelter
Share a weapon in MP
Craft 10 medicine items
Chop up 50 bodies
Revive 10 co-op players
Kill bird with arrow
Use the compass
In Single Player, kill 100 cannibals
Knock down 6 or more trees with 1 explosive. Alone in Single Player or together in Multiplayer.
Cut down 100 trees
Make and wear stealth armour
Eat an enemy
Kill a bunny. Alone in Single Player or together in Multiplayer.
Revive one co-op player
Survive 5 nights
Share a food or drink item in MP
Sleep on yacht
Survive 1 night
Sleep with another player (group sleep)