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