I think to beat mega mewtwo y, you need to have all of it's weakness. First of all, get a mega Pokemon who can beat it like mega sableye. Other dark, bug etc. Pokemon can also be used such as scyther, heracross, or slowbro. There are many other Pokemon to be used too. Also, try to get high level Pokemon to defeat it too. Basically, train hard. If your use to the game, keep up your combos and strategies within the limit. This way, he can be killed fast. Mega mewtwo is a tough Pokemon. Even after you beat him, it might take quite a lot of sessions to catch it - even with a great ball. So, good luck fighting and try to defeat him fast and quickly.
Also, try watching this video and learn the strategies: https://www.youtube.com/watch?v=D31zpV4L8-s
Hope I helped!