Mega Man 2

Mega Man 2 lets you choose eight Robot Master stages and reuse defeated bosses’ weapons in later encounters.

The stage order is part of the puzzle

Stage selection is part of the puzzle. Each Robot Master gives Mega Man a weapon that can help against another boss or a stage obstacle. Weapon energy is limited, while movement-support items create additional ways through difficult sections.

Revisit your route after a victory

A defeated Robot Master gives you a weapon another boss may be weak against. Reconsider the stage-select screen after each victory. The support items also create platforms, so a new item can change how you approach an awkward ladder or gap.

Console sequel, not arcade boss rush

This is the Famicom console sequel, not Mega Man 2: The Power Fighters, which is a separate arcade game.

Background and mechanics: Wikipedia game reference.