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