This is quite straight-forward once you have a Tank Destroyer(TD). At time of writing, every nation except Chinese and Japanese have Tier 2 TD's. TD's have a triangle by their Tier number.
Just start a game with your TD, if you get destroyed you can just go straight to your garage and pick another ready TD and play another match! It will take some time to get these two followup achievements but don't spend too much time watching games finish after you're out and it should go faster: