This requires you to beat Omega, which is found in Insomnia in chapter 14. I'd recommend being very high level (90+) for this fight, mostly so you can deal damage faster, and to have large amounts (20+) of important healing items (megapotions, megalixirs, mega phoenixes, phoenix downs, elixirs).
Omega has a fairly limited hit point pool - 555k. However, the real problem is that it is 99% resistant to all forms of damage save for electricity, and it has very high defenses to begin with.
The best way to deal damage to this boss is to use Ignis's enhancement ability to make Noctis deal damage of their vulnerability, then attack Omega's antenna. This deals quite a bit of damage, but soon it will envelop itself in a red force field that will kill you if you enter it. If you get caught, don't panic - just heal yourself afterwards.
During the rampage, Omega's defenses are far lower and you can deal much more damage. When it stops to launch missiles or shoot or do other such things, use a thunder spell on it to deal 9999 damage to it repeatedly. Eventually, Omega will calm back down, at which point you can start smashing its antenna again.
Rinse and repeat this procedure until Omega dies.