Don't let him trap you in a corner, or you will get burned. When he's on the frog, wait until he lands from a jump then get in close and hit him with two quick jumping slashes (both in the same jump) to knock him off. You can also get moderately close so the frog starts spitting fire, then retreat and hit the rider with projectiles, but it's much faster using the sword, and you'll also build some magic. When he starts bouncing all over the screen it's better to always try jumping slashes as they are safer and deal twice as damage than standing slashes. You can also try using magic. Also, on the very top of the stage there is a health item (in Easy and Normal modes), you'll have to use your rope to get it (preferably when the boss is on the frog so he won't get in the way).