First Encounter Boss Battle
During the party's first attempt to get into the Ocean Palace, they encounter Dalton for a brief moment. Dalton then summons one Golem to attack the party. This battle does not have to be won to proceed with the story, but can be won as long as the party doesn't use physical attacks. Using Magic causes Golem to have his turn start over as long as the next attack he is hit by is of a different element than the one he was last hit by, and this can be repeated with the constant casting of magic before Golem would be able to attack. Golem attacks with the magic of the element he was hit by if he is able to attack. The magical attacks are not very lethal, unlike his physical attacks.
Second Boss Battle Encounter
Boss Battle Strategy
Having finally arrived at the Ocean Palace, the party eventually runs into Dalton again, who summons two Golems to fight the party. They can be extremely difficult to beat, because there are two of them, and they are also extremely fast(Speed is probably at 16, so unless you've been really saving up on Speed Capsules, it'll be difficult, even with Crono's Swallow sword equipped. Setting the ATB mode to "Wait" might also help.) They also copy your elemental attribute of the attack you use (this applies to physical attacks as well). Also, if you went around and opened the sealed boxes in all times, and kept all the colored vests, though this yields only two of each color. Stocking up on Ruby Vests in Prehistory will suffice, as they deflect 50% of fire attacks. If Lucca is in the group, outfit her with Taban's Helm and either Taban's Vest or Taban's Suit. Equip vests, and any MP reduction accessory. Start the fight with applicable spells, e.g. Ruby Vest absorbs Fire, casting Fire on the Golems or any dual techs causing fire damage causes them to retaliate with moves of the same color, thus all Golem spells heal the party. If you have Frog in your party, a similar strategy will work by equipping two party members with the Blue Vest and the Blue Plate to absorb Water before having Frog Cast Water II.
If you lack Ruby Vests, there is one more strategy. Golem has two weaknesses: He can only copy the LAST attack he was hit with (meaning he loses the one he copied prior to that) and there is a fair time lag before he can use them. You might want to have a supply of others before trying this strategy. All you have to do is use different elements of spells in succession (example: Lightning, then Fire, then Shadow) and they will be unable to attack you. Use the spells that hit multiple enemies at once (such as Lightning 2 and Laser spin) so you can take both of them out at the same time. When each one dies, they deal magic damage to all characters, but it shouldn't be a problem if you were at full health for the duration of the fight.
Another technique to counter the Golem Sisters is to have Robo and Ayla in the party. By using the dual tech move Boogie, the Golem Sisters will be immobilized for several turns.