But wouldn't you want to live so that you could accomplish the something? It's a paradox...
No, because if the thing you are trying to accomplish requires that you risk your life, it's probably not an endeavor you would undertake if you cared about living. If you take the risk you know there's a chance you will die, in which case your goals and aspirations cease to mean anything. If you succeed, you live and possibly accomplish the thing you set out to do. I present, as a hypothetical, the movie "Short Time" starring Dabney Coleman. In this case he is actually trying to die, but I think the risk tolerance would be about the same, if not the motivation.
But even in real life, there are plenty of examples of people who would rather live, but risk their lives anyway in the pursuit of greatness. And there are almost as many examples of people who failed and died. If you don't care if you live or die, you might as well go out in a blaze of glory...