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