The quickest way I found doing this achievement was to play a local match on the KYLE difficulty and at the end of the match just click rematch and keep re matching until you complete 200 games.
If you want to keep track of how many games you have played with your character there is marker under the opponents health bar telling you how many games you have played in that session. If you plan to do this over multiple sessions I would make take a note down of how many games you plaid as there is no other place in the game that will give you that stat.
I would recommend fighting against Spinal as on average I found that he won the match the quickest as on average he took 20.4 seconds per match. I would also recommend to not choose Hisako as your opponent as she took on average 31.6 seconds to win.
Below I have included all of the average match times worked out over 5 matches against Jago on the KYLE difficulty. I have also included a video if anybody would like to see this guide in visuals.
TJ Combo: 26
Kan Ra: 30.8