Finally After waiting so long to do it After wanting to do it for a long time

"at long last" could mean 'after the long waiting' or 'after exerting effort'. it's also synonymous to the eaxpression "finally" or "at last". This is always expressed to describe exuberance toward achieving something. "after 3 attempts, I passed the exam at long last." :)

Eventually. After all of this waiting.

at long last = finally (indicates a sense of relief, as if you had been trying to get there for such a long time)