While the exact number is yet unknown, once you toss back enough grenades (frag or teargas), the Achievement will unlock. From my experience I would guess it's somewhere around 25-30, though I did not keep exact count.
In the Breakout Chapter, once you reach the prison yard you will find a lot of teargas grenades being tossed your way. Run around from cover to cover and toss them with the A button when you're prompted (standing on top of them). You don't have to toss it back, you can pitch it against a nearby wall and recover it again for faster tallying.
Feel free to drop the game down to Aspirin difficulty level, as it does not affect the Achievement.