The important thing for this achievement is that you find the cakes in the shop. The stat that's important is the +100% Yummy Cake, if the item says that, then it'll work!
You can also track your progress in the Stats tab on the main menu for AirMech Arena.
I wasted a lot of diamonds buying cakes in the player market before I realized you can buy chocolate cakes in the Decorations part of the shop for 3,000 Kudos, and you can buy more of them if you check the "checkmark" button on the left side so it will show you items you already own. Then, you can just buy some more cakes!
In fact, if you want to, you could even try reselling the cakes on the player market for Diamonds if you have enough Kudos to buy the cakes.
Once you and at least one other person have the cakes, you need to equip them in the Decorations tab for the AirMech you're using, and make sure both of you have equipped them!
Finally, play any game with the cakes equipped, and you both will get credit for the amount of cakes you have equipped! At least two players MUST have cakes equipped, or there is no credit at all.
You could play 2v2 coop, 2v3 coop, 3v3 coop, 2p survival, 3p survival, 4p survival, or any of the pvp modes to get credit for this. The more players you can get in, the more cakes you'll get counted towards the achievement.
3v3 coop is quite fast--9 cakes each time, and with an Ultimate Bucky rush it'll take about 35 seconds per game. That's less than an hour including loading times.