Dangerous Terrain

Dangerous Terrain is a phenomenon in which some portion of the battlefield between or below the hero and villain is dangerous to both parties. If Dangerous Terrain is present, be assured that at some point during the battle, the hero and villain will wind up in a shoving or wrestling match very nearby, trying to push each other into it. (In videogames, this is a Ring Out Boss.)

If the terrain is deadly and not merely injurious (a Bottomless Pit, a Lava Pit, Spikes of Doom) one can expect the villain to end up dying in it at the end.

This is a subtrope of Interesting Situation Duel.

Examples of Dangerous Terrain include:

Anime and Manga

In a sense, the Jusenkyo springs in Ranma ½ are dangerous, which is possibly why they're advertised as "a legendary training ground."
- Jusendo, the source of Jusenkyo, is explicitly dangerous. Its creators built the place as a huge maze of exploding hatches, trapdoors, dropaway floors, and hidden passages.
- The Water Citadel in the Pantyhose Taro story arc is a hollowed-out mountain, filled with water at very high pressure. Pantyhose Taro jammed logs into it and loosened enough rocks to make it into a trap for his Jusenkyo-cursed enemies, so that the slightest misstep would turn a rampaging foe into a helpless black pig, a weapons master into a duck, and an Amazon into a cat—and his nemesis into a woman. Worse, Pantyhose Taro himself turns into a gigantic winged minotaur, so splashing him would make him nigh-unbeatable. "Team Ranma" learned to mind their step across the Water Citadel in a hurry.

Film

The Princess Bride. Westley is wrestling with a Rodent of Unusual Size in the Fire Swamp. He cleverly uses one of the fire spurts to set the ROUS ablaze and distract it, allowing him to finish it off with his sword.
The third Pirates of the Caribbean ends with a ship to ship battle in the middle of a maelstrom. Instead of trying to avoid it, both ships dive in head on, trying to stay out of the worst of it while also taking down their opponent.
Tarzan's Three Challenges. In the fourth (?) challenge, Tarzan and the villain face each other armed with sabers on a net suspended above vats of boiling oil.
Star Wars Episode III: Revenge of the Sith - the lava rivers where Anakin loses his limbs.
The Flash Gordon movie has a pitched duel taking place on a constantly-tilting spike-covered platform above a Bottomless Pit.

Literature

The heroes of The Belgariad make their way through an unmarked quicksand maze and then get ambushed by mooks. One mook gets chased into the bog, rides straight off the safe path, and sinks to his doom. Durnik regrets only that he couldn't save the horse.
Not nearly as dangerous as those already mentioned: in Robin Hood stories he first meets Little John (or sometimes Friar Tuck) when they both want to cross a river on a Lumberjack Bridge; neither will back up so the other can cross first, instead they decide to have a quarterstaff battle in the middle and whoever gets knocked into the water loses.
- When spoofed in Robin Hood: Men in Tights the fight takes place over a creek just a few inches deep. When Little John is knocked off the bridge, he flops around and screams that he's drowning, and after a bewildered Robin pulls him up Little John joins him as per I Owe You My Life.

Tabletop Games

Warhammer 40,000 may very well be the Trope Namer. Difficult Terrain is the specific rules term for rubble, undergrowth, and other areas that slow the movement of troops and vehicles. Minefields and such are called Dangerous Terrain, which is Exactly What It Says on the Tin.

Video Games

Some of the stages in Soul Calibur II's story mode are like this.
The original premise of the Dead or Alive games was that it was Virtua Fighter with ~~tits~~ danger zones that send you or your opponent flying if they step into them. The developers eventually refined this into having stages that take place on uneven ground, pop-up traps, natural arenas with multiple heights that do tick damage if you fall off or get thrown off them, etc.