Power Rush is a badge in Paper Mario and Paper Mario: The Thousand-Year Door. When Mario's HP is five or lower and he has this badge on, his attack goes up by two. In Paper Mario, you can acquire it from in the library while playing as Peach. Put it into the mysterious treasure box, and Mario can get it from Shooting Star Summit's treasure box. You need one BP to equip it and you can buy it at the Lovely Howz of Badges after Chapter 2 for 50 coins and at the Pianta Parlor for 34 Piantas after getting the Gold Card.
In Paper Mario: The Thousand-Year Door, it is possible to swap your stats around via an NPC found in Rogueport Sewers to decrease your max HP down to 5. Then, you are always in danger, and the effect of this badge comes in. It is possible to have multiple Power Rush badges equipped with this strategy to constantly have incredibly high attack.
In Paper Mario