I was really determined to beat the original Devil May Cry when it came out. Me and a friend were having a personal race/competition to see who was better at the game and I remember being so hyped up to kill the boss before him just so I could say "HAHAHA YEAH, HOW YOU LIKE THEM APPLES?" When I think of games I'm determined to beat I think of one's that have frustrated me or I have something to prove to a friend, not that I didn't love DMC1. I love MGS2 but I kind of dreaded beating it because I knew the experience would end and I'd probably end up thinking "uhhh...what just happened?" (I did).
Ace Combat 5 is the closest example I can think of that fits the theme of this thread. It was a game I LOVED (and still do) and I was just sooo hyped and determined to beat the final mission and stop the giant falling satelite. The game really does a good job of pumping you up before hand, prior to the last mission, with your previous enemies joining you and all the squadrons appearing on your radar but suddenly they're like "We're here to help you, pal! Let's kick some ass!" and suddenly they turn
blue instead of red on your hud. Then you get to hear everyone talk over the radio about your squad, on the news and how awesome you are, while the remaining bad guys/people who didn't defect to the heroes' side are saying "EVERYONE, TARGET WARDOG SQUADRON, THAT'S THE ONLY WAY WE CAN END THIS", all the middle of this huge, epic battle unfolding in a city cloaked in a nuclear winter from a war that took place in the game's prologue (long story I won't go into). Then after clearing your objectives you have to fly through this looooong tunnel to destroy some reactor or gate, New Hope style, and at this point your hands start to sweat and you really feel the pressure because you're in this supersonic fighter jet going through a NARROW TUNNEL while the game's antagonist goes right in after you on your tail. So the whole time you have to control your acceleration so you don't go slam into the many obstacles inside this factory tunnel but you can't go too slow or else the bad guy will peg you with his missiles. The entire time you're weaving and narrowly avoiding death while this suspenseful music is playing and your missile warning is going off like a banshee.
That's not the end, you have one more mission after that, but instead of spoiling it ill post the music that plays:
https://www.youtube.com/watch?v=o1Qkzj5bStU