STORY-LINE BATTLES:

ALBEL 1
Galaxy: 26000 HP, 2600 MP
Universe: 39000 HP, 3900 MP
FD: 47060 HP, 4706 MP
Special Attacks: Air Slash, Charge
Elemental Defense: None
Counter Aura: Standard
Battle Trophy: Defeat Albel 1 with Items Only
This battle will come with the story line, at the part you'll have to get copper from the Bequerel mines. Albel comes along with 2 lackys. Finish off the lackys first, then focus on Albel. This battle shouldn't be much trouble.

URSSA CAVE TEMPLE
(optional - post-game dungeon)
This is a optional dungeon after the game. The monsters and bosses are quite tough here, so I reccomend doing the other dungeons first. The bosses you will fight depend on who you've recruited, and which ending you got.

Duo-battle: Albel and Romero aka 'Crafty Tag'
Battle Trophy Opportunities: Defeat Crafty Tag, Defeat Crafty Tag Taking No Damage, Defeat Crafty Tag Alone

Albel
Gal: 235,000 HP / 20,000 MP (fight 1); 520,000 HP / 40,000 MP (fight 2)
Uni: 352,500 HP / 30,000 MP (fight 1); 780,000 HP / 60,000 MP (fight 2)
4-d: 451,200 HP / 38,000 MP (fight 1); 1,071,200 HP / 80,000 MP (fight 2)
Specials: Air Slash, Charge, Dragon Roar, Hand of Doom, Double Slash, Explosion (Spell)
Elemental: Fire (Half), Water (Half)
AAA: 2-way

Romero
Gal: 100,000 HP / 100,000 MP (fight 1); 240,000 HP / 150,000 MP (fight 2)
Uni: 150,000 HP / 150,000 MP (fight 1); 360,000 HP / 225,000 MP (fight 2)
4-d: 185,000 HP / 230,000 MP (fight 1); 460,800 HP / 382,500 MP (fight 2)
Specials: Crimson Sword, Flashing Sword, Sword of Darkness
Elemental: Water (Weak), Everything else (Half)
AAA: Homing

These kind of fights depends on which characters you've recruited from the four available ones; Albel, Nel, Pepitta and Roger. You'll fight the two characters you haven't recruited. Both battles also have a side kick. In case you haven't recruited Albel, one of these two battles include him. You'll fight him along with the demon Romero. Romero's a fairly hard opponent since he has sudden attacks and he's fairly fast. Albel himself isn't very threatning, though he has the ability to cast Explosion. You might want to do MP damage to Albel. If you keep your character's HP up and keep your characters moving, you'll be fine.

Fayt and ? battle
You'll at least fight Fayt in this battle. The other person you will fight depends on which ending you got. Depending on what you picked in the PA's, Fayt can have an ending with every 8 of the playable characters. This character will also be his teammate for this battle. If Fayt happens to get a single ending, Luther will be his teammate. But this an Albel shrine, so I'll only discuss the battle with Albel.

Fayt
Gal: 700,000 HP / 70,000 MP (pre-MoT); 1,000,000 HP / 100,000 MP (post-MoT)
Uni: 1,050,000 HP / 105,000 MP (pre-MoT); 1,500,000 HP / 150,000 MP (post-MoT)
4-d: 1,505,000 HP / 150,500 MP (pre-MoT); 2,300,000 HP / 230,000 MP (post-MoT)
Specials: Side Kick (W), Blade of Fury, Air Raid, Ethereal Blast, Lightning Strike (Spell), Laser Beams (Spell)
Elemental: Fire, Wind (Half)
AAA: Star Guard

Albel
Gal: 940,000 HP / 80,000 MP
Uni: 1,410,000 HP / 120,000 MP
4-d: 2,133,800 HP / 176,000 MP
Specials: Air Slash, Charge, Double Slash, Dragon Roar, Hand of Doom, Explosion (Spell)
Elemental: Fire (Half), Water (Half)
AAA: 2-Way

You'll be in for a long battle. Especially Fayt is tough because he's so hard to fight and he's fast. So he's much harder then any of the previous bosses in this temple. You might want to complete the other dungeons first and then go back to fight Fayt. The only strategy I can give you is to get rid of Albel first.

RECRUITMENT-BATTLE (Optional)
This is in case you've screwed up getting Albel at the Kirlsa Training Facility. You still have the opportunity to get him. When you've been to 4D-space, you can get him anytime when you're back on Ellicoor II. Go to Kirlsa and talk to Woltar, then head over to Crosell's lair in the Urssa Lava Caves. Fayt will have to fight Albel one-on-one. When you win, you can let him join your party. Depending when you do this, you'll get Albel 2, 3 or 4. These battles shouldn't be much trouble if your Fayt has done enough leveling-up.

Albel 2
(Available on disc 2, before Sphere)
Gal: 50,000 HP / 10,000 MP
Uni: 75,000 HP / 15,000 MP
4-d: 91,000 HP / 18,500 MP
Specials: Air Slash, Charge, Double Slash
Elemental: Fire (Half), Water (Half)
AAA: Standard

Albel 3
(Available after Sphere, but before retrieving the Sacred Orb)
Gal: 120,000 HP / 60,000 MP
Uni: 180,000 HP / 90,000 MP
4-d: 223,200 HP / 126,000 MP
Specials: Air Slash, Charge, Double Slash, Hand of Doom
Elemental: Fire (Half), Water (Half)
AAA: 2-way

Albel 4
(Available any time after retrieving the Sacred Orb)
Gal: 340,000 HP / 120,000 MP
Uni: 510,000 HP / 180,000 MP
4-d: 669,800 HP / 288,000 MP
Specials: Air Slash, Charge, Double Slash, Hand of Doom
Elemental: Fire (Half), Water (Half)
AAA: Wide Area Homing

Information gotten from Gamefaqs.