Monster Hunter 2, in the Training Arena with a Gunlance against a Tigrex (which is probably the most vicious enemy in the game). Low health, no healing potions left, less than two minutes on the clock. The Tigrex isn't showing signs of low health, either. Seeing it turn around in preparation to charge, I steel myself and charge as well. We meet halfway in the arena, me fully expecting to be killed by the monster. Instead, the lance goes straight into its head and kills it, completing the assignment. Best feeling ever.
Also, in the same game, completing the mission 'Four Horns' (kill a Diablos and Black Diablos in 50 minutes) with less than 30 seconds remaining. Good times were had.