* 우승 (useung): This means "victory" or "winning." It's often used to refer to *winning* a championship, rather than the championship itself. For example, you might say "우승을 차지하다 (useung-eul chajihada)" which means "to win the championship."
* 챔피언십 (chaempyeonsip): This is a loanword directly from English, and it's perfectly understandable and commonly used. This is probably the closest direct translation.
* 리그/대회 우승 (ligeu/dahoe useung): This translates to "league/tournament victory." You'd use "리그 (ligeu)" for a league championship and "대회 (dahoe)" for a tournament championship. This is a more descriptive way to say it.
Therefore, depending on the nuance you want to convey, 챔피언십 (chaempyeonsip) is the most straightforward, while 우승 (useung) is commonly used in the context of *winning* the championship. Using 리그/대회 우승 is best when you want to specify the type of competition.