Darkness Rising, another tune fitting of its title and the games it goes with.
This game also has its "epic-style" tune... in two different styles! Skyward Bound for a more energetic style and Don't Look Down for a more laid-back style.
The real star of this game, though, is Bowser's Revenge. One of the most frantic and intense BGMs out there, for some of the most frantic and intense mini-games ever devised for the Mario Party series.
Bowser's final boss theme. It naturally wouldn't be a Mario game without an epic theme accompanying the King of Koopas. At the end of his rope, Bowser realizes he has no further defenses, and is ready to duel with everyone currently present, and he will stop at nothing to make sure his plans succeed. The dark, somber music definitely reflects that, and makes a good theme all on its own. With the final few bits of his health remaining, Bowser triples in size and makes things much harder, making sure not to go gentle in the face of his opponents. The music's change in tone from somber to intense and dangerous seals the deal; either your mission will fail and Bowser gains the power of the Mini-Stars, or he falls once again and gives up the final remnants of the huge power he once had at the beginning of this journey. A fitting end to the last boss of the game.