There are 3 phases involved in the fight in Normal mode, and Hard, Very Hard, and Ultimate hit you with the somewhat harder 4th phase. Dark Falz will rain Rafoie, Rabarta, Grants, and Megid on you, but I'll tell you what to worry about in each difficulty. I'd like to point out that Rafoie will never be a big threat.

Hunters:
Completely rid of yourself of anything that hits multiple enemies (Slicers are fine; I'm talking about Swords and Partisans). You will not need to worry about hitting multiple foes at once. Bring a good Handgun, as back-up.

Rangers:
Bring your good Handgun and Rifle and stick to them.

Forces:
As stated, Dark Falz will not use anything physical on you, so bring along a Wand. If the Darvants are giving you trouble, equip a Rod instead. Set your controller configuration to fire off Barta, Zonde, and Gizonde. In Hard Mode and later, you are encouraged to bring along weapons that boost Foie, Barta, and Zonde techniques.

Defensive Strategy:
The spiky little things will be all over the place, but you really don't need to panic since they're pretty weak...unless they get a mass horde going. Just make sure to alternate between dodging them and briefly referring to your radar to find vulnerable Darvants (they are the brighter circles seen on your radar; the darker ones refer to invulnerable ones that you must avoid).

Offensive Strategy:
Hunters/Rangers: You must only do a Weak-Weak combo attack or a Weak-Strong attack and that's it. Don't you dare do a three-hit combo! You'll want to save the least smidgen amount of HP and TP for later.

Forces: Barta is your friend. You should be able to defeat a Darvant with one Barta attack. This is where you want to use a Rod.

Defensive Strategy:
The chariot will fire off Darvants throughout this phase. It is seen that it will fire them off either when it has stopped moving after switching places around the arena, or when it has been continuously attacked. The Darvants have slightly increased stats in terms of DFP and HP, but their elemental resistances stay the same.
Dark Falz will fire off Rafoie and Rabarta when he's not angry. Rafoie can just knock you down, and should not be a big worry. However, Rabarta is the bigger threat: not only can it freeze you in place, but the game can glitch itself and make it appear as if two Rabarta attacks hit you, and knock you out (it is VERY annoying when it happens). You are encouraged to bring units and protective gear that reduces Ice damage (use Resist/Blizzard units if you got them).
Lastly, if you keep going at it, Dark Falz will fire off his sky beam attack. Immediately heal yourself when you see this happen.

There is a way to stay safe for a good portion of the fight. If you're a Hunter and want to do this, I suggest you bring a Handgun along. During the fight, try to sort of get behind one of the heads on the side of the chariot. When Falz starts moving, there is a chance that you might be dragged along with him, and be pushed behind, making you safe from his Rafoie and Rabarta attacks! However, the sky beam can still hurt you (I think), and the Darvants can still get to you.

Offensive Strategy:
Hunters: Only one of the heads should be lowered on the chariot for parts of the fight. This is the only head you can use a melee weapon on. If you want to be safe and not chance it, use your Handgun on one of the raised heads. You're pretty much hack-and-heal.

Rangers:
Your Rifle will help you a lot here. Stand at a distance and fire away. Don't be afraid to shoot out Darvants. Feel free to try and get behind Dark falz.

Forces:
You will be using Zonde on Falz. If the Darvants are close, Barta them. Now, like other bosses, Dark Falz has that nifty Gizonde trick going (just like the Dragon, De Rol Le, and Vol Opt, Gizonde can hit multiple areas of their bodies). Dark Falz is somewhat trickier to do, as it is harder to pull off. If you're willing to sacrifice the TP, Gizonde away. If not, just Zonde Falz, Barta the Darvants, and heal every time you are hit. Oh, and that Rabarta glitch might get you.

Hard/Very Hard/Ultimate Strategy:
No changes here. DF might get stat boosts, but you can take him down quick.

If you're in Normal Mode, this is your last phase to do. If you're not in Normal Mode, you're part-way done.

Defensive Strategy:
Falz will now rotate along the outer radius of the arena, and he'll do more of it as it is weakened. Only when Falz is in place will it do any attacking.

Now, Dark Falz will randomly alternate between Rafoie and Rabarta, but it is done more often. Again, that Rabarta gltich can have a higher chance of happening here. You can actually determine what attack he'll use: if he aims with his right "arm", he'll use Rafoie. With the other "arm", Rabarta. And yet again, as it gets weaker, the sky beam attack will start to occur.

Dark Falz will also randomly "stomp" the arena. If you are close to Dark Falz, you will get Slow, which will hinder your attack efforts.
Lastly, as Falz is very close to dying, he will steal HP away from you. It's not big of a deal: simply recover and take the time to get in as much damage as possible. You might just be able to cancel out his recovery.

Offensive Strategy:
Hunters: Use that Dagger or Saber and wail on him, but the Slow status might get in your way. You could use a Sol Atomizer if you have a couple and willing to expend them, or just use the Handgun throughout the entire fight. You can use Zonde to deliver a bit of damage as it moves away.

Rangers: Rifle it. You've got the range and power, so all you pretty much have to do is aim and fire. You shouldn't even be close to Falz to get Slow.

Forces: Falz is weak to Barta now, but don't throw away Zonde off your configuration. Simply run up to Falz, staying a bit off to the side (a possible thought had occurred that if you stayed a bit off to the side, the Rabarta glitch might not occur), and launch Barta as much as possible. Heal yourself after every hit. When Falz starts to move, fire off a few Zondes.

Hard/Very Hard Strategy:
Minor change: the harder the difficulty, the faster Falz will move around the circle. Use your judgment to guess where he'll be stopping at.

Ultimate Strategy:
You know, I've yet to face DF in Ultimate, so I'm taking what I've seen in Version 2: besides the fact he'll be insanely fast around the arena that it's impossible to catch up with him, he just might scare you with a new Darvant attack. Instead of Darvants coming at you, four of them will mysteriously rise out of the ground and slash you right in the middle. But it seems to happen if you just stand still for awhile (only while Falz is attacking as well).

Note that you'll only see this form in Hard Mode and later. If you were in Normal Mode, congratulations.

Defensive Strategy:
Falz just loves to keep you on edge. He's going to be invincible for most of the fight (unless you're a Force), and you're required to have...patience. =P
Dark Falz will just deliver a crushing slash on your character. This always does a set amount of damage for each difficulty, so if you have some units to boost HP, that's just dandy. After that, he'll proceed to wander around the inner radius of his new torus-shaped arena.

When Falz takes to the sky, his next attack is a slew of blue orbs. The deal here is to immediately start running at a slight arc, perpendicular to the radius of the ring (to clarify: if you are facing Falz when he launched the orbs, and you turn left, you'd be running slightly to the right; if you turned right, you'll be going slightly left). After that, Falz will launch Grants. This is where you need units against light. Resist/Holy is your best unit, but you'll need to buy Resist/Saint units from the armor shop if you haven't found Resist/Holy (and they ARE rare...I've seen 4 of them since the start of my Gamecube days).
When Falz is near death, he'll share your soul. Any damage delivered to Falz is reflected on to you, so halt your attacks (but you can get out of this; more on that later). When Falz takes to the sky, he'll cast a Megid spell that won't do anything (yet). Then Grants is cast. After releasing your soul, he'll always do his physical slash.

Offensive Strategy:
Hunters: Melee is a no-no. Grab a Handgun and do it as soon as Falz is open. If you can cast Foie, do so.

Rangers: Rifle it again. Fire Foie if you can.

Forces: Do NOT say you do not have a Club of Laconium yet. You should have found at least ONE by now. Equip the Club of Laconium and fire Foie no matter what. Dark Falz's invincibility does not protect him from magic, so keep firing it off.

Very Hard Strategy:
Just make sure to have more HP.

Ultimate Strategy:
Falz didn't get much of a boost from Very Hard. The only new thing to worry about is the Megid attack: it WILL work in Ultimate. Just dodge it and continue the fight as usual.

While Falz "shares" your soul, you can use a Handgun (or Rifle, for Rangers) that steals HP. Continously fire the HP-stealing attack to hurt Falz, but also restore your HP, even though you get hit. This helps speed up the fight.