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