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