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