There's no opportunity for any player to do anything between the Trapeze Artist's chaotic, orblike entrance and it returning to its owner's hand if unsuccessful.

If Trapeze Artist is a token, use a printed token or another Magic card to execute the flip.

To "turn over completely" means to do a full 360° rotation. Trapeze Artist should start with its back facing the table, then at some point midflight its front should face the table, and then its back should once again face the table. That's the minimum for a successful entrance. More flips are optional but encouraged.