Minecraft wiki entry for Player_versus_Player, associated text: The Nether: Use a Knockback sword, Punch bow, or even the knockback from charging your opponent to knock them off a higher platform. With luck, they will take significant or even lethal amounts of fall damage. Or they may simply fall into the lava ocean that lies below! Bonus points for knocking them onto magma blocks or finishing them off from above with a bow/crossbow/trident. Soul Speed will be especially useful in a Soul Sand Valley, and you can use that to your advantage.
The End/End City: Use a Knockback sword or Punch bow to try to knock your enemy off the island. If you are in an End City, lure a shulker into hitting your opponent, which will inflict Levitation, sending them into the air and disorienting them. You can then shoot them repeatedly with a ranged weapon. Once they fall, finish them off with a trident, sword or axe.
Dimension Explosives: In both the Nether and the End, Beds are a deadly explosive weapon if you can get the timing right. The deadliest strategy involves knocking the enemy up elevated terrain with your sword and/or axe before intentionally exploding a bed next to them on the elevated terrain while they're still in midair (make sure your feet are below the bed when you blow it, otherwise the recoil damage may end up killing you instead!) This will massively damage/kill the enemy, and you don't really receive much recoil damage. A downside to this strategy is that the fires after the explosion may burn some valuables the enemy/enemies are carrying. Respawn Anchors in the End or the Overworld are also an option, but are more expensive and takes slightly longer to activate. However, Respawn Anchors are stackable which make them more reliable for endgame combat. The need to charge Respawn Anchors can also be negated by pre-charging them outside of battle and breaking them with a Silk Touch Diamond/Netherite Pickaxe.