He's the first master you'll have in the game. You should be at least LV5 before he takes you in as a student. For more information about different masters, kindly refer to the Masters Basics page.
00. Become Piccolo's Apprentice
You need to reduce his HP in an one-on-one battle against him. After this, you'll learn the Ki Blast skill "Evil Explosion"
01. Burst! Evil Explosion!
Make sure you have Evil Explosion equipped in your skill set. Whittle Piccolo's HP until he's down to critical health. Now time your attack and use Evil Explosion to defeat him.
After completing the scenario, you'll learn the Ki Blast skill "Super Evil Explosion"
Item Request
Back in the city, talk to Piccolo again and he will ask for an All-Energy Capsule S. If it's not available in the item shop, check if you have the materials to craft it in the Mixing Shop. Give it to him to get his [Master] Z Soul "I'll make you a fine demon!"
02. Attack of the Three Piccolos!
Skill: Light Grenade
Fortunately, even when there's three Piccolos you have to deal with, they won't be that aggressive that they'll gang up on you and prevent you from making your combos. You'll be comfortably fighting against them one at a time, with the occasional interruptions. Defeat all three of them to complete the training mission.
03. Mastery
Skill: Special Beam Cannon
Before Piccolo gives you the final training, you have to equip Light Grenade. Fight him and damage him with normal attack. When his HP is critically low, find your timing and finish him off using Light Grenade. Since Piccolo is the earliest master you'll encounter, this fight can be particularly easy especially if your level is already high.