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All information c/o GameFAQs, taken from the walkthroughs by A l e x, gsninja and kratos15354.
Yggdrasil
Type: Angel
Hit Points: 40,000
Experience: 8320
Tech Points: 3000
Attack: 1800
Defense: 380
Weak: Dark
Strong: Light
Finally a battle against this guy where you actually have to win. That's a bit easier said than done though, he can put up quite a fight. That's not to say he's the hardest boss you've fought either, while he is consistent with his attacks, none of them in particular will be the party obliterating spells you may fear. He also doesn't block too much or have particularly high defense. If you're able to get in with a couple of good fighters you can actually juggle him for quite a long time, that way you'll be doing good damage, and won't have to worry about dodging his magic at all.
Yggdrasill will cast Ray, Holy Lance, Thunder Arrow, Ground Dasher, and maybe some other spells from a distance and will use Death Eater and Outburst at close range. Death Eater is a mini version of Judgment which may give you some magical ailments. Outburst is a blue version of Explosion, but is unblockable, even with a guard tech.
Mithos
Type: Human
Hit Points: 55,000
Experience: 8280
Tech Points: 5000
Attack: 200
Defense: 410
Weak: None
Strong: Light
This guy is hard. Really hard, even at a high level. This Holy Lance spell devastates, and his Judgment spell can eliminate your entire party if you're not careful. He also has a lot of HP and almost unbreakable defenses meaning this battle will take a long time. Consider using an all divide if you can't seem to stay alive. The only decent ways of damaging him really are unison attacks and high level magic for Genis like Explosion. The other thing you need to watch out for is the Retribution spell which will put adverse status effects on your entire party. You absolutely need to command Raine to cast Nullify after that or you'll find yourself crippled for the rest of the fight. Good endurance is the key to winning this battle.
He has most of the magic techs that he used when he was in Yggdrasill form: Photon, Ray, Holy Lance, Ground Dasher, and Indignation. However, instead of Outburst, Judgment Ray, and Death Eater, Mithos has Judgment, Absolute, more physical attacks (which are basically bursts of light energy), and his most ridiculously cheap attack: He sends a light wave across the battle field that inflicts one or more physical AND magical ailments on every single party member. This is the attack that will use up a lot of your time curing the ailments, while Mithos is already charging up for another attack, and it sucks when he uses Judgment after it.
Mithos is an annoying little brat in and out of battle. He will always be resistant to light and darkness, but you must defeat the Judged, Fugitive, and Neglected to remove the rest of his resistances.
Immediately following that battle... is a second form!
Mithos
Type: Unknown
Hit Points: 60,000
Experience: 0
Tech Points: 1500
Attack: 2150
Defense: 265
Weak: None
Strong: Everything
Same Mithos, new body. This fight is just like the Judged, Neglected, and Fugitive. He will mainly cast mid level spells while you're happily pounding away on him. His melee attack is making a ball of light in front of him that will hit you several times, but it's easily blocked.
In this form, Mithos loses a lot of his good attacks, which are: Photon, Ray, Holy Lance, Judgment, Absolute, and Ground Dasher. Instead of those, he gets: Thunder Blade, Spark Wave, Flame Lance, and Explosion. He retains one of his original physical attacks, and now also employs normal blade attacks. Mithos has also become slower, which puts him at a further disadvantage.
I will ease your mind right now and tell you compared to the last fight, this is much much easier. It's still no walk in the park of course, but if you can take on his first form, the only reason you have to lose here is if you ran out of HP/TP healing items. There are only two hard things about this boss: First, he still has Judgment, so he is capable of dealing massive damage to your party. Be sure Raine is always ready to Revitalize. Second is his most powerful attacks are all close range, meaning you will likely find Lloyd killed more than a couple of times, but it won't be your entire party, so it shouldn't pose a problem. He seems to have an objection to blocking, because he never does it. Use this to your advantage and despite his 5000 HP gain on his first form, you'll find he'll probably go down in barely half the time.