Cool game overall! Had fun playing it.
One thing that would make all the difference is having some feedback in the shop. Now I don't know how many gems I have and if I have enough for an upgrade there is no feedback when you buy something. So for now the best strategy is to click a few times on each and hope you bought as many as you could.
Also, currently there is no decision to make in the shop. You may or may not want to change that. Because the gems and upgrades are linked you just buy as many as you can from each. Instead there is a decision to make in which gems you go for. But since those are randomized and some are in places which are obviously not worth going for, most of the time the gem colors don't matter in my decision and whichever color I get is up to luck. And also you only have a split-second to decide which gems to go for.
On another note, it's an interesting idea. Every level you have to choose between risking your time and getting another gem. Great job!