Saw a post on Reddit saying it this Gilgamesh thing is doable with one off-realm MONSTER DPS with the appropriate realm chain. I was skeptical but tried with Rem (Sync+Awakening+USB1+HA) and I managed to beat it with some mistakes made with my FF3 team which is pretty weak.

OK with Entrust + Wrath
Luneth basically did nothing except use the RW chain plus my FFIV Historia crystal to break rage
Ingus got his Awakening off and immediately died (did help with some extra reflect damage)
Arc Hastega/Curada and her USB to heal with. No dive on her at all.
Rem with HA and Sync, AASB and USB1

Ingus activated historia crystal right at the start (error should have waited to break a rage with it), OK just wrath'd until 4 bars, entrusted to Rem and Rem blew USB1, Sync, AASB and then went to town with her HA. Luneth activated the chain right before the AASB (another error should have waited a bit since it ran out near the end) and then just used the crystal to break the rage at 50%. Arc healed as best she could but was pretty sketchy considering how weak she was. Thing is Rem just tore him apart.

Just remember to hit him with the weak realm people before your monster or it'll go to the wrong realm.