In order to catch a fairy, you need to buy in a store or find a Fairy Ball at the location, with the help of which fairies are caught, each ball has its own level from level 20 to level 40 and above.
After you have purchased the Fairy Ball you need, feel free to go to battle. Leave the enemy 10% of life and the Fairy Ball will light up in the upper right corner, then immediately run to the enemy until he escapes from you into the portal, just be careful that he does not cause fatal damage to you and grab it like an ordinary coin and the ball will catch his. This is where the fight will end, after the results of the battle you will be offered to leave the fairy or let go of the choice.
You probably noticed luminous balls in the arenas, so if you understand that you are losing, then fly tighter into this light and in this way you will be saved from death by flight.