The only levels that you need to die are:
1-3
1-4
2-2
3-3
Making with 26.
Plus you can beat the last level with 0 deaths too.
Just need to get back in the log (just give it a initial swing and let it spin =D).
Some nice tips:
For HARD badge don't need all level to be 3 stars
You can let 2 zombies pass and still get all 3 stars.
Magus shots faster with 1 bullet only!
Don't forget to realod befor last boss so you don't get memory leak near the end.
Don't try to kill the boss without almost all upgrades are in max lvl. (it takes 2:40 min to win lvl 15 for $30,000.00 gold and 5 to win lvl 16 for $1,500.00 if you lose) I've done the level 15 5 extra times.