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