The fight with Mundus during mission 22 will be divided in two stages: Space and Lava cave.

The hardest and most frustrating aspect of this fight is that those two successive stages have to be completed with no checkpoint between them. You will likely die and retry quite a few times.
 

Space

The Space part is kind of a shoot 'em up sequence. While avoiding his attacks, you have to shoot at him to charge your  gauge and then use a DT attack (which can't miss) to deal him serious damage. Most of what he sends at you can be avoided by moving around the screen and you can keep shooting meanwhile; only the massive laser attack requires you to roll to not get hit. If you destroy the spheres that have a glyph on them, you will charge your gauge more than with a direct shot at Mundus. Finally, the more DT glyphs lit you have, the more devastating the attack you inflict him.

Lava Cave

In the Lava Cave, its weak point will be its chest. He will summon some of these glyph spheres for you to charge your gauge and activate DT, which is essential to dealing significant damage. To hurt him with some swords slash, wait until after he punches and got closer so he's in your range or jump on the big chunks of rocks he raises and get at him from up close. You can also shoot some charged meteors at him, but that is not the most efficient attack. You can also deflect his white energy shots back at him with a well timed sword slash. That is pretty much it. Oh, it seems that if you shoot the lava dragon he calls, you get a green orb (a very small consolation...). And do not fall in the lava, you will get hurt.

It is probable you lost your patience at this point, but it is possible to beat him fair and square without using any items, like in the video below. I must confess I did not even give it a try in DMD; 10 devil stars for the first part, 4 untouchables for the second and he was history without breaking a sweat!