Here's a clip showing me getting an S-Rank and a T-Rank in the first round of the Cooking Challenge mini-game in chapter 3 of "Deltarune." To get an S-Rank, you need to get at least 500 points in the mini-game. To get a T-rank, you need to either get 640 points or completely re-fill the popularity meter by feeding the special guests.
Also, as you can see in the final score of round 1 in the second clip, you don't need to get a T-rank in two or three of the categories listed on the Evaluation chart to get a T-rank in the first round. It seems like you just need to get a T-rank in the mini-game and get a secret bonus to get the best ranking.
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