How can I get higher grades in fights?

Merely completing the fight without getting hit is not enough to get a grade higher than B. You need to also use your various gadgets and special moves to complete this task. Doing this is called the "Variation Bonus"

Examples of moves that will increase your Variation Bonus:

• Quickfiring gadgets (using Batarangs, Batclaw, Explosive Gel, etc.)
• Ground Takedown (Crouch + Counter on a stunned enemy with stars around his head)
• Unlockable Takedown moves from the upgrade tree
• Other combat moves (Aerial Attack, Glide Kick, etc.)

As long as you use different moves to hit enemies and don't get hit more than once or twice, you should get an A grade. If you complete the fight "perfectly" by using lots of different moves and never losing a combo, you'll get the highest S (apex) grade.

This also goes for predator encounters. Using different ways such as Inverted Takedowns or Tightrope Takedowns to take out enemies will earn you a higher grade and more experience.