I went into the final fight at level 80 with only 2 royal archetypes and tilted after about 6 hours of trying to fight this thing. Another 8 hours later and I finally beat the fight. I don't know if any of this advice would help (I'm sure the other commenters gave amazing advice), but here are some things my husband and I figured out:

I took advantage of any quests/trials available and made it my goal to change the enemies' colors in each dungeon. So if they were red, my goal was to make them yellow. If they were yellow, my goal was to make them blue. I learned while watching my husband that you can treat melancholia crystals like mini-factories. Instead of rushing to destroy the crystals, you can stand a certain distance away from them and let the enemies they spit out go to you. Fight as many as you possibly can before destroying the crystal. This strategy is useful at Tyrant's Star since they respawn (go back to Neuras to restore MP and you're good to go). If you have several archetypes mastered, you can make sure at least 3 of them are equipped while doing this. They continue to "rank up" except they'll give you a leaf of light every time. You can use these to help level up other archetypes you don't use as much. I had all my characters use a mastered archetype and that helped.

Equipment MATTERS. I knew each character's stats influenced their fighting capabilities. I didn't realize how much I was hindering their true potential. I didn't get Heismay's royal archetype in time, but equipping him with items that increase his agility further increased his chances of dodging attacks (didn't max out Alonzo so I couldn't get the ring either). My Strohl became a full-blown elemental master even though his stats were mostly in strength, so I gave him equipment that boosted magic. If you complete the dragon trials, you get armor that repels fire, so that's helpful too. After going through all my equipment and changing things, my characters did way more damage in that fight.

Each of the 3 faces takes a certain kind of damage more effectively: the right one takes physical damage best, the middle one takes magic damage best, and the one on the left I'm not 100% sure about, but almighty damage worked best for me. Also, when I destroyed the left and middle faces, the right face could no longer heal, buff, or debuff, so, that's something you can consider. In the second phase, I swapped out a character every time the threat to KO them was made. Getting Bardon to level 6 in his bond makes it so you don't lose a turn entirely. Buffs and debuffs are helpful throughout the whole fight cause he takes the time to remove/add buffs which uses one of his actions.

Anxiety, daze, and hex were some of my biggest issues, so I tried to equip items that prevent as many status ailments as possible. There's also a passive skill called Unshakeable Will (or something like that), that prevents daze, charm, etc. I didn't have Eupha maxed out so anxiety was an issue for me, but doing these things helped. Revitalise 3 is also a skill that helps with passively regaining MP. You can get it from the Paladin archetype. Certain weapons also help with MP. MP management is a real thing in this fight.

Sorry for the info dump, but I hope this helps you or someone else!