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