Subterranean Pavilion is a secret stage unlocked by completing 16th Archaeological Expedition's Excavation Site (Leo's Stage) on the hard difficulty. This is unlocked by beating the game, and can be selected immediately after completing the last mission. After completing this stage on hard, you'll have a secret route available. Simply beat that stage and you have your trophy!
Just for the record, if you are defeated upon reaching the boss you hit a checkpoint of sorts. When you hit "retry" you'll start there and be able to fight the boss again. This comes in handy especially if your partner has taken too much damage.