If you make it through the fifth chamber with some decent health and armor this fight can be pretty easy. It can also be horrible. Honestly blanks might be more important than health if you have good reflexes.
The normal phase of the Dragun has several easy to dodge attacks, and a few not so easy.
1) Fire Breath: he usually starts with a variation of this, either sweeping left to right or just shooting straight down. The horizontal sweep is much easier to dodge as you can just jump through it, but the straight down blast takes some jukes.
2) Uzi Spray: pretty straight forward, if you stand in the bottom middle and roll up the middle you'll be fine
3) Pistol Spray: This is a tough one, depending on the previous attack these stick around for a while, producing concentric rings of bullets. Use blanks.
4) Homing Skulls: fires 5 homing skulls down from the middle, burst them down. Dragun has a nasty habit of pairing this with other attacks like bouncing bullets, speaking of which
5) Bouncing Bullets: this attack sucks, Dragun fires down toward the player with bursts of bouncing rounds that typically bounce off screen before catching you in the behind. Depending on your health it may be wise to ignore the Dragun for a hot second and just focus on the bullets.
6) Knife Turrets: the Dragun throws a knife into each wall that fires tommy gun spreads at you. On their own the spread is easy to dodge, if you stick to a wall as i do they usually pass over you. Its of course pairing with whatever Dragun is doing that makes them tough to deal with. Burst one of the down so you have somewhere to hide. As far as I can tell he won't do it again until they're both dead, but killing them both is highly advisable, fewer bullets, fewer problems.
7) Wing Attack: Dragun flaps his wings summoning two waves of bullets to fan down on the player. This attack is weird, as it comes down from the top, and then sweeps horizontally across, generally missing the bottom-most corners. That isn't much help though, as its coming from left and right simultaneously. I can't say it enough, use blanks.
8) Rocket Launcher: Dragun fires a missile at the bottom of the screen, erupting in 4 waves of bullets. A good dodge puts you past them all though, this is a lot less scary once you know the timing.
If you've been firing at him this whole time (or have some sweet companions doing the work for you) and his health has decreased to about 10% congratulations! This is the second phase. The Dragun will summon hundreds of bullets with convenient holes you must dodge your way through. Blanks are quite ineffective, as they only clear out a small circle around you and not the whole screen. After you dodge all of those the Dragun's heart is exposed, so lay into it. It usually takes 2 waves worth of damage to kill him. During this phase the body of the Dragun is completely invulnerable except for during the exposed heart bit. So don't waste bullets.
Here's a video showing off some of the attacks and what getting really lucky with items and guns looks like.