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