Here is the full list of all 11 Bonsai achievements.
Grow many different trees
Prune lots and lots of branches
Chop off your trees at the trunk
Grow a Birch
Prune lots of branches
Grow a Japanese Maple
Grow a Sycamore
Grow a Sugar Maple
Help a tree to grow fully into adulthood
Prune some branches
Grow an Oak