Due to level 1-1 not starting its timer til you serve a meal, you can just cut a bunch of shrimp and fish and once you have a good stack built up of each, just start serving the meal required. I did this with a buddy who brought me fish from the other side and was doing between 50-65 per round. If you do it solo it will probably be more in the 30-40 range but still by far the fastest way I've found to grind this out quickly.
Would recommend this being your last achievement since by the time you get everything else done you should have between 500-650 meals served depending on how many levels you have to redo for 3 stars.
Note you have to be the one actually delivering the dish to the window for it to count.
Update. Cclan2 says the game could stop tracking so double check your progress. If it isn't tracking restart your game.