Here is the full list of all 10 Jump/Boxer achievements.
Beat the fifth stage with less than ten deaths.
Beat the fourth stage with less than ten deaths.
Beat the fifth stage.
Beat the fourth stage.
Beat the third stage.
Beat the third stage with less than ten deaths.
Beat the second stage.
Beat the second stage with less than ten deaths.
Beat the first stage.
Beat the first stage with less than ten deaths.