Video Tutorial: Walkthrough
This fight is actually more of a puzzle than an actual battle. At the beginning you'll see him at the end of a large hallway. When he sees you approaching he punches the wall in futility. Notice that his eyes will always turn red before he makes any attack. Just hide behind a pillar and make your move when his head is looking elsewhere. Your pathway will be blocked with rubble. You have three options to clear this rubble:
Any large weapon dual handed even if you do not meet the stat requirements will allow you to destroy the rubble with one hit with R1 attack. Equipping Eternal Warrior's Ring may be helpful and make sure not to wear any equipment that reduces stamina regeneration. Lighter weapons
You can safely hide behind a pillar and cast. Use something cheap like Soul Arrow, Fire Spray, or Flame Toss if you have it (Flame Toss is best for melee characters, as you'll use up less MP). You'll need maybe 5-6 Fresh Spice to refill your MP as you go. This way the boss won't even make a single attack.
Coax him into attacking the rubble for you
You need to be quick for this, and able to manipulate the camera at will to see when he has committed himself to an attack. You might notice that his eye color may change from yellow to red once you come out of cover. If you stay out of cover too long, then he will attack you. Try to get into cover ASAP when his eyes are red, then run again when his eyes turn yellow.
Your first move will be to progress down the hallway to the right. Your goal is to reach the upper platform, it is safe there, with the glowing ballista. Push the button on the side to shoot the boss and reduce his health by a third. He'll punch the area in front of you and clear a path down some stairs and towards the second ballista platform at the far left of the area. Clearing your way through the second level is much easier, as the dragon will occasionally wince in pain from the massive spear in his side; this is your chance to clear rubble. If he sees you, he will stop wincing, so make sure he doesn't see you or this will be a lot harder.
There is a Crystal Lizard by the second ballista. After the second shot the boss' head will be pinned down on some lower dirt ramps. Since he has been gravely injured by taking giant spears straight to his body, he will be breathing heavily. His breath is hot and will burn if it touches you. You can melee his chin horn, backing away each time he breathes out. Alternatively you can use arrows or magic (Soul Arrow/Soul Ray for instance). Lock on and attack his horn. Every couple of hits, he will raise his head in pain and then it will fall back down to the ground. Lock on again and repeat.
The Atlus wiki reports that a couple of players who died at the same time as the Dragon God dies, have not been able to proceed to the game's end event. The players were able to collect the dragon god soul, but were still not invited by the Maiden in Black to finish the game. Make sure you do not risk dying when taking your last hit at the Dragon God. Ranged attacks will help. If you must melee, go in with a Second Chance or Warding and full health.