♪MUSIC♪ Demo challenge

That's the boring way yes. For style points youd most likely pick a wad where the length of the song is about the length it takes to play to map. (Most songs are around 4 minutes, so you'd have to be pretty speedy for the most part)

If you have to hang around the map a little, plan to do something interesting to consume time like cause the monsters to infight, use a weaker weapon, or find all the secrets, collect all the items, etc.