Chaining is timing your character's hits to alternate landing on your enemy to gain a damage bonus for every hit you land. The max damage bonus from chaining is 4x which your big hits do even more ridiculous damage. There are several ways to increase the chain bonus
Regular Chain = .1x for each alternating regular hit
Element Chain = .3x for every alternating hit of the same element.
Spark = .8x for attacks that land at the same time.
So what you do is get 2 characters to build your chain up to 4x then mix in a finisher to take advantage of it. This video
explains chaining mechanics but has an example of how a chain can boost the damage of a finisher.
This is how folks do a ton of damage with characters in the game.
Okay. So I was thinking correctly. I chain attacks all the time, though I generally go from lowest ATK to highest so the last hit in the chain is the character with the highest ATK. It's too hard to worry about that every time I attack, so I let things go as they will and not worry about it. Since I don't really bother with this kind of stuff seriously, this information doesn't really mean anything to me. My top damage dealers are still CoD and Lightning. I find that Chizuru isn't all that great since she doesn't have a big damage move (that I can see).
Of course, that does remind me. What is supposed to be Chizuru's big damage move?