Here is a listing of some Killer Move combos that are used by the fighting characters of the game. In order to chain two Killer Moves together, you must have the Link Combo accessory.
Claude is perhaps the best Link Combo user in the game as many of his moves come out pretty quick and are easily combo-able. His combos do the most damage out of the rest of the characters by sheer number of hits alone and has almost no recovery time for most of them. All in all, he is one of the best.
Shooting Stars + Burst Knuckle
Shooting Stars + Mirror Slice
Shooting Stars + Twin Slash
These are pretty effective combos that'll cause major damage to the enemy and even more so if the enemy is trapped against a wall. An excellent chipper to use.
Burst Knuckle + Mirror Slice
Burst Knuckle + Twin Slash
Another effective combination as the Burst Knuckle comes out pretty fast and is Cancellable, plus the other moves come out quick too.
Air Slash + Head Splitter
Air Slash + Ripper Blast
Alright combo. Most effective as a long range attack as the Air Slash will keep the enemy stunned long enough to hit it with your Head Splitter. The latter can be used as a multi-enemy attack up close. I rarely use these though.
Sword Bomber + Twin Slash
Sword Bomber + Dragon Howl
Anti-air is all you can say with these, plus it keeps Claude at a safe distance away from the enemy.
Dragon Howl + Twin Slash
Dragon Howl + Mirror Slice
Dragon Howl + Ripper Blast
These are pretty effective combos as the first two stun the enemy long enough for Claude to pull off his next move unscathed and the last one is a long-range attack. Works well on those damn bunnies that jump around a lot.
Mirror Slice + Burst Knuckle
Mirror Slice + Shooting Stars
Mirror Slice + Twin Slash
Some more excellent combos as the Mirror Slice comes out quick and is cancellable and does tremendous damage. Excellent wall trappers too.
Ashton is just as good as combos as Claude and does just as much damage, but his combos have some serious lag and recovery times, leaving him wide open for a counter-strike, so you have to make sure Ashton is a good distance away from the enemy so he can pull them off.
Cross Slash + Twin Stab
Cross Slash + Hurricane Slash
Alright combos to say the least, though he needs to be some distance away so he won't get hit out of it.
Leaf Slash + Hurricane Slash
Leaf Slash + Sword Dance
Pretty good combos here. Leaf Slash will teleport him in front of the enemy and the other attacks will put on additional damage.
Dragon Breath + Piercing Swords
Dragon Breath + Northern Cross
Dragon Breath + Cross Slash
Dragon Breath will hit the enemy from afar, letting Ashton charge in for his close range attacks. You can also trap enemies with this as well. Be warned, Dragon Breath takes some time to use and leaves him wide open for a counter attack, so you got to be a good distance away.
Hurricane Slash + Sword Dance
Ashton's equivalent of Claude's Mirror Slice combo and one of the best combos he has. The Hurricane Slash comes out pretty fast and knocks the enemy in the air and Sword Dance will catch them on the way down. A nice combo indeed.
Bowman is not an easy character to chain Killer Moves with, as most of his moves won't go well together. I haven't played with him as much, so forgive me for the lack of evaluation on Bowman.
Spirit Attack + Firebird Attack
Spirit Attack + Poison Pills
These are good keep-away combos that Bowman has. When powered up, Spirit Attack will hit the enemy 3 times and the other attacks will tack on more hits to ensure that the enemy is a safe distance away.
Whirlwind Fist + Sakura Attack
This is the only multi-hit combo I know of that Bowman has. Whirlwind Fist will knock the enemy in the air and Bowman will chase it with Sakura Attack. Sometimes this won't work as he'll knock the enemy too high to hit with Sakura Attack.
Precis is a good combo linker, while considerably better at it than Bowman, she's not nearly as good as Claude or Ashton. She'll need someone to back her up so she won't be attacked once the lag sets in. As of now, I have yet to see Precis's Barrier and Mujin Super Beam moves, so I can't comment on those until I see them.
Rocket Punch + Ally Oop!
Rocket Punch + Parabola Beam
Rocket Punch + Bloody Mary
Rocket Punch + Bang-bang Attack
A nice combo for Precis similar to Claude's and Ashton's long range-short range combos. Rocket Punch will hit them from afar, stunning the enemy long enough for Precis to run in and pull off the next attack.
Parabola Beam + Ally Oop!
Parabola Beam + Bloody Mary
Parabola Beam + Bang-bang Attack
These are good long-range combos for Precis that keep the enemy at bay, though the last on on that list is similar to the Rocket Punch combo as it'll stun the enemy long enough for Precis to get close and do some damage. Use these when you're facing really tough enemies.
Since all of Opera's moves are long-range, there aren't many effective Killer Move combos she can use. Again, I have not used her much in my game, so forgive me if I haven't found that many combos with her.
Flame Launcher + Alpha on One
Spread Ray + Alpha on One
These combos will ensure that Opera is a good distance away from the enemy, but with the exception of Flame Launcher, she has to be a good distance away from the enemy to pull these off or she'll get hit out of it.
Photon Prison + Flame Launcher
Photon Prison + Alpha on One
Photon Prison + Spread Ray
Photon Prison will freeze the enemy long enough for Opera to pull off the next move, but seeing as though Photon Prison isn't really that effective, it's pretty much useless.
Ernest is an okay combo-linker. All of his Killer Moves are designed to keep the enemy a safe distance away, so his moves will be useful when you're fighting a really powerful enemy. He is ideal for this since his moves don't take that much MP.
Thousand Whip + Dimension Whip
Good anti-air priority and multi-hitting ability. This is one of his best combos he has. I haven't played with much to learn his other moves so this is the only one I know at this time.
Chisato is the female counterpart to Claude in terms of Killer Move combo ability, although not as strong as Claude himself. She has effective short and long-range Killer Moves that'll rack up a lot of hits in a short amount of time.
Twister + Whirlwind
Twister + Rising Dragon
Perhaps the first combo Chisato will learn. Twister will hit the enemy lots of times, then the second move will come in and hit them some more. If you want to get the enemies dizzy, then these are the combos to choose.
Whirlwind + Rising Dragon
This could be Chisato's best Killer Move combo she has. There is almost no delay between the moves and both are fast and strong. You may want to turn off Strong Blow if you wish to get the maximum effectiveness out of it.
Tear Gas + Flame Thrower
Good combo except the wind up time may not be advantageous as the smarter enemies can just move out of the way. You'll have to move closer to use Flame Thrower, but hopefully Tear Gas will have dizzied the enemy long enough to use it without harm.
Ten Thousand Volts + Burning Cards
Chisato's multi-direction combo. Similar to Claude's Ripper Blast move, this'll rip up a multitude of enemies stupid to walk in it's path. A must have if you wish to clear the screen in a snap.