There are several
tried-and-tested devices used by video games regarding final bosses :
The Teaser : Sometimes the boss will appear briefly and unkillably earlier in the game, only to retreat. (A la Double Dragon, Streets Of Rage 3, Thunderforce, etc.)
Multi-stage boss : Just when you think you've finished the boss off, they return in another form (Shinobi, and Treasure games were notorious for this).
The conveniently located stock of power-ups : Whenever you stumble across a large cache of goodies in a game, you know there is a seriously tough boss just around the corner (Doom).
Chase : After disposing of a particularly tough boss, you have to shoot down his "escape pod" (or equivalent) within a set time limit. The most infuriating example of this is Rockman The Power Battle where Dr. Wiley almost always manages to evade your clutches.
Respawning henchmen : Often, the task of dodging bullets (or equivalent) was made all the more difficult by a constant stream of lesser enemies being spat onto the screen.
Some other well-known bosses are Mr. X (Streets of Rage series ... there is always an equivalent "Crime Boss" character in every scrolling beat-em-up, a tradition started by Double Dragon and carried on by Final Fight), The Spider Mastermind (Doom), Dr. Robotnik (aka Eggman), Dracula (Castlevania) and Mother Brain (Metroid).