So, due to some heavy drinking between George RR Martin and William Goldman, the Red Viper and the Future Dread Pirate Roberts come to a misunderstanding. Oberyn thinks Inigo is an agent of the Lannisters responsible for her sister's death. Inigo believes Oberyn killed his father. They fight to the death.
Inigo gets his trusty fencing sword, while Oberyn gets his Dornish spear (it's not coated in poison because, frankly, it's kinda pointless here). No BFR, all fights to the death.
Scenario 1: Battle takes place in the same King's Landing arena where Martell fought the Mountain.
Scenario 2: Battle takes place in the same environment where Inigo Montoya battled the Dread Pirate Roberts.