To get this, complete one of Rextro's arcade games, then select to do it again. It will display a leaderboard. Complete it again but aim to beat the top score.
If you do the race arcade game in world 1, you need to complete the race with MORE than 2:30 on the clock. There is a shortcut across some planks with 2 enemies on it. You do not need to do the shortcut every lap, but doing it at least twice will give you some room for error.
If you are doing the Glaciator arcade game in World 2, you need to score more than 1400 points. When you reach 1400 by collecting feathers, stop collecting and jump onto one of the elevated platforms on the left or right of the screen and stay still. The enemies cannot reach you here