This will most likely be your last achievement, simply because it's going take a very long time. Nothing really to say for this one except just keep playing those matches! If you can complete an Arms Race match quickly, then that mode would be best.
A better way to do this, at least currently unless patched, is to leave your Xbox running while you are idle and let the bots play in Arms Race on Expert. There is a glitch where if you are playing (or idling) offline with bots in Arms Race, one match will count as two. I would recommend idling this whenever you are not on your Xbox (while sleeping, eating, out somewhere, etc.), because this may end up becoming patched.
As far as the achievement itself goes without this glitch, I would suggest leaving idling the matches as sort of a last resort until everything else is done.
Nevander Credits: Ayx for the "better way" mentioned above.