The Collaborative International Dictionary
one-up \one-up\ a. Ahead of a friend or competitor in some competitive activity.
Wiktionary
alt. (context idiomatic English) To outdo, to do something slightly better than a competitor's prior effort. n. (context video games English) An additional life or an object that increases the player's number of chances or "lives" by one. vb. (context idiomatic English) To outdo, to do something slightly better than a competitor's prior effort.
Usage examples of "one-up".
The angriest mob, and the one moving with the most sense of purpose, was moving directly toward the orphanage where Alvin had been unable to resist showing off by one-upping Calvin's fixing of the man's foot.
Could Covington be that shallow, that she would go to such efforts simply to one-up a personal enemy?
Or, just as often, individuals had a satori-like experience and then used it to bolster their preexisting stage of adaptation: a businessman used the new freedom to return to the office and more aggressively one-up his associates.
He'd have to buy a riding mower to one-up her on this, and since his lawn wasn't any bigger than hers, a riding mower would be an expensive sop to his ego.