JUNGLE RELIC CHARIZARD
Wait until Charizard breaths fire into the air and the fireballs fall on the stage. The is where you have to get creative. By purposely running your styler into the fireballs around Charizard you can open up enough room to easily circle him and complete the capture.
SEKRA RANGE CHARIZARD
This one is beyond simple. Grab a Poliwhirl on your way up the mountain and hold on to it until you reach the Charizard. Once the capture starts, IMMEDIATELY use Poliwhirl's Poke Assist. With one well place bubble the capture is a cinch. (NOTE: If the Charizard breaks out of the bubble before you have a chance to capture it do not worry; it has a habit of walking around after it breaks out allowing you a few seconds to finish those last couple loops.)