A Timed Boss Battle pits the player against either an invulnerable foe, environmental hazards, or limitless enemies in which the only way to proceed is to withstand the nemesis or obstacle(s) for a set period of time (lest ye perish). The crux of this gameplay element is that the player is almost always unaware that the battle is timed; ineffectively exhausting all attack options until the (hidden) timer runs out and a cutscene is shown. Furthermore, upon replaying—and thus, one would hope, being aware of—a timed boss battle, there is little to do but patiently avoid conflict and conserve items or ammunition. This example is derivative of the unwinnable battle.
Another type of timed battle, usually in tactical games, requires the player to “defeat all enemies” in a limited number of moves or rounds (sometimes termed “days”). In this case, the player is fighting against the clock.
There are, of course, several multiplayer timed battles in a wide variety of games ranging from Super Smash Bros. to Carol Vorderman's Sudoku. These are commonly selectable from a menu and not an element of a game's storyline. Furthermore, the timer is usually visible within these modes, and can help as much as hurt.
Similarly, 2D and 3D fighters are almost entirely comprised of timed battles in which the timer doesn't favor a specific opponent.