Magus doesn't up his defense when he gets ready for Dark Matter. He drops it.
Magus lowers his guard to cast a spell!
Well... actually no. That SFX is used when he is about to cast his strongest magic attack - but it is also used when he increases is magic defense (one of his actual techs). It all depends on whether he is casting the spell or not... so who really knows.
From the ending... it sounds like this from beginning to end... (I do not know if the ending SFX is randomized)
Magus: Fire2
Frog: Normal attack with Masamune
Magus: Magus attacks multiple times with Scythe
Magus: Dark Mist
Frog: Water
Magus: Increases magic defense - Or powering up for Dark Matter attack
Magus: Lightning2
Frog: Critical hit with Masamune
Magus: Dark Bomb
Magus: Dark Matter
Frog: Frog attacks multiple times with Masamune
Magus: Geyser from blue flames
Frog: Normal attack with Masamune
Magus: Casts spell... then the ending enables
As you can see, Frog got OWNED by Magus and Frog barely even touched Magus. Maybe his last spell teleported him out of his castle in shame, or transformed him back into a human. However, aside speculation, the real victor is up to the player to decide for sure.