Nox Suzaku is one of the two optional bosses in the game and can be encountered during the second playthrough, or New Game+. Make your way to Chapter 6 and choose the second option when presented with a choice, allowing you to do "The Last Line of Defense" mission. At the end of this mission, you will be reintroduced to Nox Suzaku, who you might remember as the black creature during the first mission.
Once you complete "The Last Line of Defense", Nox Suzaku will be in the wild, although you can’t actually confront him just yet. If you didn’t get the airship, Setzer, yet, then you will need to get that, with it being obtainable during Free Time 7.2. See the relevant section for details. After that, keep fighting enemies and harvesting Phantoma until you notice the Phantoma going up into the sky, triggering Nox Suzaku’s appearance.
Nox Suzaku is level 200 on Cadet and Officer (and level 250 on Finis), and utilizes a mechanic in which it stays hidden until someone is killed. Thus, you’re going to need something to buff yourself with Reraise, with the only two options really being Phoenix Pinions or Anima Lanterns, the latter which can be farmed from Tonberries.
You will also want to be as close to level 99 as possible and have great magic damage, meaning Rem is a great candidate for the battle, since her magic is naturally high. Although it isn’t needed, Ultima will make the battle go quicker, which is unlocked by earning a cumulative total of 150,000 SPP to get the spell.
As for equipment, you will definitely want something that gives you Freecast and something else that gives high defense. If you can manage to clear the Tower of Agito, you will get the Agito Insignia, a great accessory. Additionally, if you have Ultima, then you should have access to the SP Crystal, another fantastic accessory for this fight. Avoid is a great magic to use as backup, which you should have by now (get from Moogle in Fountain Courtyard at 10 hours of gameplay).
Battling Nox Suzaku
Upon ramming the creature with your airship, you will be transported into an arena with three shadowy figures. The fight with Nox Suzaku is a special one, as it will not show itself until one of your characters dies and only then, it will be for a few seconds. That’s your only chance to deal damage to Nox, which is where the Reraise effect comes into play.
There will be three rounds of three enemies each, with the first two being copies of your own characters. For the final round, there will be a Behemoth, as well as some other enemies. Defeating all groups of enemies will cause Nox Suzaku to retreat, meaning you’ll have to harvest Phantoma until it appears once more.
Although you can do the battle at any of the three rounds of enemies, it might be best to defeat the first two to go to the third, as the Behemoth is a lot slower than most of the other enemies you will fight. Take down all enemies except for the Behemoth, then when you’re ready, let it kill you (make sure you have Reraise!) to make Nox appear.
As soon as you die and get revived, spam the down button on your D-Pad to use one of the Reraise buttons before your brief moment of Invincibility wears off, then quickly target Nox Suzaku to attack it. All that’s left is for you to repeat this over and over until Nox Suzaku finally goes down.
Note: Although you defeat Nox Suzaku, it can appear again, even in the same playthrough. It’s possible to fight it multiple times, as it will still steal your Phantoma once you reach a certain amount.