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