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.
Set off 20 bombs
Cut down 1000 trees
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.
Repair a shelter
In Single Player, kill 100 cannibals
Craft 10 medicine items
Revive 10 co-op players
Grow all plant types
Build a super long wall
Kill a bunny. Alone in Single Player or together in Multiplayer.
Sleep on yacht
Finish Game
Share a weapon in MP
Collect all robot pieces
Make and wear stealth armour
Use the compass
Collect all cassette tapes!
Share a food or drink item in MP
Kill bird with arrow
In Single Player, don't kill any cannibals for more than 10 days in a row
Revive one co-op player
Survive 5 nights
Cut down 100 trees
Survive 1 night
Sleep with another player (group sleep)
Eat an enemy
Eat an entire family
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
Killed downed enemy with rock
Chop up 50 bodies
Kill 6 or more fish with a stick of dynamite. Alone in Single Player or together in Multiplayer.
Find all missing passengers
Eat all mushroom types
Pass 50,000 steps
Catch fish with a trap. Alone in Single Player or together in Multiplayer.