Low Level Run

Low Level Runs involve getting through the game, with the lowest possible stats/equipment/weapons that you can get away with. They are quite common in RPG style games, where leveling up is prevalent.

Examples
Most games in the Final Fantasy series have challenges like this associated with them, as well as the Kingdom Hearts series. Pokèmon, Neverwinter Nights and the Elder Scrolls series are also well known for utilising these challenges