I played through the Time Attack a couple times and learned that the game doesn't have a place to look up your individual records on the mini-games. the game lumps all your times into a total each play through of time attack and it doesn't separate the records out. Also if you get a record in a mini-game and then quit part way through the time trial the game does save your record, but it doesn't show it anywhere except for when you start up another trial and start playing that mini-game you got the record in.
Here's my time trial records:
Ballistic Beach 40.68
Pizza Me, Mario 51.38
Jigsaw Jumble 23.93
Flinger Painting 16.10
Pit or Platter 33.71
Chain Event 22.41
Upward Mobility 21.73
Peak Precision 7.56
Snow Go 37.33
I didn't include Speeding Bullets, because my 26.60 record is better.