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