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