This is easily done on Mission 3, but it can only be done once you've already completed the level once.
Once you've completed the level once and have your angel boost ability, load up the level again. Kill the first group of enemies. Kat will call out to Dante and have the symbol prepared for him to leave. The floor will fall and Dante will say he'll need to "find another way." Because you already have angel boost (the ability required to leave the level), simply angel boost your way through to Kat to exit the level. This skips 95% of the entire level and you'll be able to snag this achievement no problem once the stats screen boots up.