From the Super Mario Wiki
Peekaboo is a badge in Paper Mario and Paper Mario: The Thousand-Year Door. In Paper Mario, it can be bought from Merlow for ten Star Pieces, and in Paper Mario: The Thousand-Year Door, it can be bought from Dazzle for seven Star Pieces. If Mario equips it, the HP of all enemies are displayed at the start of battle even if they haven't been Tattled by Goombario or Goombella. This badge also applies to other objects that usually do not display their remaining HP even if they can be tattled, such at Koops's Shell Shield.
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