i played through the entire game, thinking that you get both upgrades everytime you one. It took me until afterwards to relize that you have to choose one and click it.
all you have to do is use booster+pierce at top, skip a column, boost, slow, eye if needed, then top it off with a slow. skip another column, and do the same thing for the fourth column. Then for the last one, do the same thing as the first, just facing left. then just stand on the first or second tower and swing your sword.
you don't learn spells, once you have one, you drag the spell over your character and as long as you have enough MP, you'll cast it.
Also, if it takes you a few tries to get far, its okay. I tried about 5 times, not getting further than floor 6, and all of the sudden, I'm at 40 and going strong.
this game has a good variety of towers, upgrades, ect. but it is way too easyl. all you have to do is spam snipers everywhere, dont even have to upgrade them. Yes, i bat the entire game this way.