You know what I think about the hair of Kratos about your image!
It is funny but if you didn't said this graphic effect was for eruption, I wouldn't have guessed, I would have thought it was for an other attack, which is called flare tornado, I don't know if you know this attack. And it is funny also to see that this graphical effect looks like a lot Ho oh's (I don't know if I spelled it correctly) attack.
But I have to say something, this is not something bad, it is all the contrary. But when I see your Dark serpent move, I immediately think of one of Yuri Lowell move, in the japanese version, he has a thrust and the graphical effects look like a little of this move, especially with the color in fact because when he does this move, his sword transform in a triangle of this color. I don't know what name has this Yuri Lowell move but anyway, it is a good move that truly matches Kratos!
Edit: Ok. I just tried this character, and I have some things to say, keep in mind that I only give my opinion.
About A attacks alone, when you press A some times, and when you hold A after the three combos, Kratos makes quick slashes, you probably know what I'm going to say, but again, I don't think Kratos can make so quick slashes like this. We can keep the idea, but reduce the speed of these slashes. And I wanted also to say about this attack that it is strange that even if we don't keep the A button pressed, he continues to do it, I only say this because I've never seen a move like this in Brawl. For example, correct me if I'm wrong, to do multiples Fox's kicks, we have to keep the A button pressed. The last thing about this move is that I'm sorry if I comment it only now, but I don't remember these quick slashes to be in previous version, but maybe I'm wrong, maybe I didn't pressed the button correctly to use it. Honestly, I don't know!
About Light spear as up B, it jumps pretty high!
It is not a real problem because this is the only move that kratos has to come back. But I don't know if it allows to grab the platform, I didn't saw to be honest. But what is strange about this move, again I might be wrong, I didn't see a down slash like the one I see on your image. What I saw was a move a little similar in fact to Victory light spear because he makes a thrust in fact as final movement! Again, I will verify because I find this very strange!
About his waiting pose, and this I'm pretty sure I didn't noticed it earlier but was there, Kratos crosses his arms, but we can see the sword or it should be invisible as it is in Kratos's sheath. I know, this is not a real problem especially we don't see so often waiting animations but I just wanted to say it.
An other suggestion I can make is to edit a little his pose when he casts Judgement, Explosion, and Thunder Blade only when he casts these three spells. Look at the pose he makes when he casts these three spells, and look especially his hand. It is pointed down, my suggestion is to point his hand up, and open his hand if it is needed so that he makes "5" with his hands. This is the way he cast spells in the anime.
There is also an other problem about Dark Serpent, when you do it after this move you can run, but if you run just after this move, you run much faster than the normal run speed. To run after Dark Serpent, you have to maintain B button, and besides press the stick. If you do this, you can run just after Dark Serpent.
The biggest problem excepted the down smash, of this Kratos is about Dark Serpent move. This move is really good, it matches Kratos perfectly, and I don't have to complain about what he does if we maintain B, that is not a problem. The true problem in fact of this move is in air. Indeed when he uses it in air, he uses it normally, but if you don't keep B button pressed, when he touches the floor, we can't do anything! There is one of Kratos knees that is vibrating, but we can't move or anything and if I recall correctly, we can hear the sound of charging movement. This is a glitch, which can be annoying... So if you can fix this, it would be really good!
Oh, and I wanted to ask you, have you changed Fierce demon fang properties a little? I wondered this.
The last thing I have to say is about lighting blade chaining with super Lighting blade. A very good thing, again, we have to know how to do it but it is true it would have been difficult to put it using different conditions. A,d there is something that made me smile about this chain, this is something that kratos uses often, true, and obviously it made me smile, but you kept Marth's spirit about this chain, I mean, to touch the opponent twice, we have to be at good distance, and that is what made me smile, it is so funny the influence that marth had.
Anyway, you made a good job, there is still work to do, but this Kratos is good. But please, if you do one thing the next time you come, fix the dark serpent glitch!