"Irregardless," though a "real word," is often considered to be grammatically incorrect. I, in fact, cringe whenever I hear it; many people will judge as being incorrect and it is far from being accepted in speech, much less in writing.At least in American English "No matter what" is more common. Saying "no matter what happens" carries a little more gravity, like something terrible could actually happen.
In a very academic setting an entirely different construction might be more appropriate. In this case, the adjective "irregardless" could be a good alternative.
Hope that helps.