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