In a game where it is easy to repeat levels and/or boss battles it would be really great to have different methods for beating the same boss that yield different outcomes and rewards. This idea comes from a combination of Starfox 64 and Ulduar from Wrath of the Lich King.
For example, a boss that has 3 "henchmen" that can be battled individually before the actual boss is engaged. Defeating the henchmen before fighting the boss will make for a fairly straightforward fight, but if you engage the boss while leaving one or more of their henchmen standing, the encounter changes in some way and can become more difficult based on which henchmen you don't fight ahead of time and supremely difficult if you leave them all standing.