The Crystal Sage in Dark Souls III can be found in the forest area right before the Cathedral of the Deep. Upon entering the arena, the Crystal Sage will likely attempt to cast some spells at you. He’ll either try to hit you with slew of purple projectiles, or cast a purple laser beam at you. The laser can be easily dodged by rolling to either the left or the right. For the projectiles, simply wait until the last second before dodging, as they’ll home in on your position.
The Sage doesn’t have a lot of health, so you should be able to whittle him down fairly quickly. Each time you attack him, he’ll teleport away to another spot in the arena, so keep a keen eye out for where he goes. Whenever he teleports, he’ll also summon blue crystals from the ground to block your way, though these can be easily destroyed with a swing of your weapon.