When you're in a kart not only can you go fast, you can jump too. So for the Yellow and Blue dungeons you can Kart jump your way to the end until you get to the boss. However, the only downside that comes with this is turning. If you get stuck in a corner or run into a wall, you could lose a lot of time when trying to turn out. If you somehow get in that situation, get out of the kart, leave the wall or corner, and immediately jump back in. With enough optimization you can breeze through the first three rooms and get to the boss.