The verb overshoot means to go beyond some target or goal, further than needed or wanted. "He was trying to land the airplane, but he overshot the runway and had to try again." "He was trying to put his golf ball on the green, but he overshot it and landed in the sand trap." An overshooter, I suppose, would be someone who overshoots. However, I've never seen it used that way.

You may be thinking of the term "overachiever" which is someone who does more then the required amount of work to succeed.