The Hot Potato powerup only shows up on the battle table. It looks like a fireball, and is an instant power up (ie not one that you can save for later use). When a ball runs over this power-up that ball changes into a 'hot potato' that is identifiable by its sort of glowy, rainbow trail. When this ball drains on the opponents side of the table, you steal double the usual penalty in score from your opponent and make progress towards the trophy. Note that the hot potato power-up will not spawn if you have the penalty set to 100%, so make sure that the penalty is set to 50% or lower if you want to make progress on this. This trophy is cumulative across all games, and will award in middle of the game, as soon as you score the 30th hot potato.
Given how rare the hot potato power-up is to even spawn (it seems the most rare), and the fact that just collecting it is only the first step (you then need to hit that ball over to the other side of the table and have it go past your opponent) this is the most grindy of all the achievements on this table. Therefore, you should not go specifically for this achievement until you have all the other battle-table ones done, and while going for those others, just keep in mind to try to collect and score any hot potatoes as come up during this time using the methods detailed below.
When going for this trophy specifically by far the easiest thing to do is to use two controllers, so that there is nobody on the other side of the table so that any hot potato you hit over to that side will have a 100% chance of counting towards the achievement. If you have to play against AI, make sure to set it to 'easy' as this will give you the best chance of scoring. The AI method is not recommended as this might take up to twice as long. Since these count across multiple games the exact target you set it too is fairly irrelevant, though I recommend 10M score and 50% penalty as it would be a waste to collect a hot potato (or have one spawn) but have the game end before you can score it (this is fairly unlikely though). If you have everything else done other than this trophy and arcade rat ('play 30 games'), it would make sense to play several shorter games, however.
The key thing when grinding this out, is to have the view zoomed so that you can see the entire table and to always be watchign for the hot potato powerup to spawn. You have only a short time to collect a powerup once it shows up on the table (about 15 seconds?) before it vanishes so act fast, and obviously this will go better if you are practiced at making the pinball go where you want it to go. After collecting the powerup you then need to hit the ball over to the other side which hopefully you have some experience at. If you are on the left table and catch the ball on the left flipper aim for the pass through located just above the pistol, if you catch the ball on the right flipper aim for the saloon ramp as the ball always exits the saloon to the other players side (reverse these instructions if you choose ot play on the right side). The ball can also change sides in the drain area (under the flippers) but this is not a recommended method to aim for as the price of failure is a lost ball. You can also stockpile ball thief powerups and though it seems that ball thief does not work to steal powered up balls (need to confirm this) what you can do is if you see a hot potato pick up spawn on the opponents side you can quickly thief his balls and then use his flippers (if you are playing in 2P mode) to try and collect it with your color ball or hope the opponent hits your ball into it and subsequently loses it (if you are versus AI). If you happen to be playing against the AI (hopefully while goign for some other trophy) and it hits a hot potato (of his color) over to you you can try and capture the ball using the capture hole under the upper left flipper (left side of table) and it will remain as a hot potato but change to your color and you can try and hit it back.
I earned approximately half to two-thirds of the progress towards this trophy while going for others, and then got the remaining in about 2 hours of grinding specifically for it using the methods detailed above.