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