The easiest way to do this is solo with one chef.
Load up level 1-1, grab a piece of food and then stand facing one of the kitchen units straight on. Make sure you're not facing into a diagonal corner as the food can get stuck.
Then, simply alternate between X to throw the food and A to pick it up back up. The food will land on the kitchen counter when thrown and can be picked up quickly.
This is much easier than throwing to the other chef, pressing RB to swap, making sure they are aligned and throwing. They have a habit of throwing to the side and missing or needing realignment which wastes time.
achievement first, so then you have 250 throws done at the same time as the catches, then start throwing at the counter instead of the other player for the remaining 250 throws.
The achievement trackers do track the progress of the throws and catches, however the tracker only seems to visually update at the end of a round. You will earn the achievement when you hit the 500, but if you wanted to check the tracker to make sure it is working, you would need to restart or quit to see the progress bar move.