Gigapede has several attacks, most of which can't hurt you if you are standing on an elevated platform.
Lightning pulse: Gigapede causes a wave of electricity to run along the floor. Being off the ground avoids this completely.
Lightning bolts: Several vertical beams of lightning form below Gigapede and try to home in on your position. Staying off the ground floor renders this attack harmless.
Purple orbs: Gigapede fires multiple purple spheres of energy at Dante. These orbs can travel through Gigapede, and can hit Dante even when he is standing on the top level. Move quickly to avoid them, or attack them to send them back at Gigapede.