In-game dialogue:

Cloud of Darkness

Vs Onion "You cunning little brat."

Firion

After beating Kuja "I guess you weren't prepared for me?"
Vs Squall "I'll have you know that I do not lose."
Vs Warrior "Let's give this all we got."
After beating Warrior "I still need to be stronger."
Vs Zidane "Let's have a fair contest."

Garland

Vs Cloud of Darkness "Ah, it's the monster who enjoys destruction!"
After beating Cloud of Darkness "Hahahahaha, know your limits!
Vs Jecht "So it's the man who got himself trapped in the spiral of death!"
After beating Jecht "That was a boring battle."
Vs Firion "It is futile to fight on faith alone!!"
Vs Squall "I've come to challenge the heart of the lion!"
Vs Ultimecia "Why don't you show me how you pass through time!"

Kuja

Vs Firion "It's said the weak dog barks the most."
Vs Squall "All of that self-confidence... let's see if I can break it..."
In battle "Keep dancing, hahahaha!"
In battle "Lo~ok out!"

Onion Knight

Vs Garland "Don't boast just because you're so big."
Vs Tidus "You won't feel tired if we work up a sweat, right?"
Vs Ultimecia "Mind hastening my time with you?"

Squall

Vs Firion "I won't lose to you."
After beating Garland "This is like talking to a wall."
Vs Warrior "I won't go easy on you"
After beating Warrior "Good thing you aren't my enemy"
Vs Zidane "I'll be your opponent."
After beating Zidane "Guess I should've gone easy on you."

Tidus

Vs Garland "Think you can tire out someone as energetic as me?"
Vs Squall "If you got something to say, say it!"

Warrior

Vs Firion "Emotions alone won't bring you victory!"
Vs Garland "And now is the hour of destiny!"
Vs Squall "Do you know that true power comes from preparedness?"
Vs Zidane "Don't think you'll steal a victory from me!"

Zidane

Vs Squall "If I win, I get to keep your sword!"
In battle "Too slow!"
In battle "You missed me!"
source: ffchaoticcosmos: In Game Dialogue + IGN Report