A quite simple stage. Start out moving while taking in consideration the enemy's range and the terrain you're standing on.
On this stage you can obtain your first Equipment, that can heal HP only once. This is the main difference with Reimu's route.
If Momiji's HP goes too low, she'll retreat. Keep her HP above 3000 to avoid this.
To deliver the final blow, use Marisa's Narrow Spark and Nitori's Monster Cucumber together. (For this you need both characters on adjacent squares and Marisa must attack first. Nitori needs to be in range as well.)
However, being in position to do this may prove hard since once you attack her, Momiji will constantly move towards you.
On Lunatic, Momiji won't wait for you to attack her to move, and she'll start moving on her thir turn.
Save and Load a lot if you have problems while attacking the fairies. Also make use of Nitori's Iron Wall Seishin for safety.
If you feel gutsy, or you have too much troubles while getting in range for the finisher, you can use Extending Arm + Magic Missile instead, but you'll need to pray for a critical hit.