Everything in the Heckran Cave is vulnerable to magic, and resists Physical attacks. It's almost like it's a test of your new magic skills! Despite not having magic, Robo is not useless here, because "Magic" means any elemental attack, and his Laser Spin counts. Likewise, Techs like Slash and Flame Toss are effective. Just keep an eye on the party's MP, and especially Crono's.
Save and use a Shelter before facing Heckran. Use Magic on him, and don't attack when he's taunting you. It's a pretty simple fight.
You'll find a whirlpool at the back of the cave that leads to the area near Lucca's House. Stop in while you're in the area.