As undrentide-san pointed out, ~しようとしても is a conditional of ~しようとする or "to try to do," and often connotes that the trial fails.
どんなに勉強しようとしても、できなかった。
No matter how much I tried to study, I couldn't (e.g. because of sleepiness).
On the other hand, the main clause following ~しようと conditional expresses the state after the thing is done, as same as ~しても.
どんなに勉強しようと(=勉強しても)、上手にならなかった。
No matter how much I studied, I couldn't become good at it.