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