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