Complete arena training course was a mission in Jak 3. After being rescued by the people of Spargus, Jak was forced to take the Arena of Death's training course to prove his worth before the eyes of king Damas.
The first mission introduces you to the controls. They're identical to the ones in Jak II and this mission covers all the basics. Simply follow the on-screen instructions and collect all the tokens. You'll eventually reach the highest point of this structure. The test dummies you'll see along the course don't have to be destroyed, but do so if you're not yet familiar with the combat controls.
After completing it, you'll be immediately head into the next mission "Earn 1st war amulet" after a cutscene.