I just thought I'd share some info with anyone wanting to improve their times in the Dragon Kart mini-game from the corresponding side-quest.
(1. Absolutely wait until you've gotten to chapter 15 and beaten the last racer to acquire/fully upgrade the final kart, the "Rising Dragon Kart."
(2. Basics: To get a boost start, hold accel. about midway through the 2's animation of appearing then dissolving, so just about before it starts to dissolve. Collecting 10 rings brings your kart up to it's maximum top speed, so aim for a line that gets you 10 rings as soon as possible, or as easily as your skill level will allow, and then aim for as tight of a line as you can, ignoring extra rings. You want to be boosting as much as possible, that means touching boost pads/using boost items at the end of a boost or a combined boost. (More on that further down.)
Double boost pad bringing my kart up to a max speed of 90:
(4. Due to the way the drifting mechanic works in this mini-game, I would highly recommend making quick, sharp movements, changing only your timing and severity of your angle of approach. (When you choose to start your turn and how hard you turn.) Z-drifting is absolutely necessary on some turns and it is good to note that some turns may require multiple hops during a Z-drift and the like.
(5. {!!!Raised terrain is your enemy!!!} Do not, unless boosting and going along the line of, and not in need to turn against, drive on raised terrain. (You go slow.) You can hop to avoid the oil or slime (maybe sand) patches pretty easily without losing too much time. I recommend boosting over sand patches as much as humanly possible. (So far most lines I've encountered have boosts through sand.)
(6. Remember that not every lap is the same, so get used to some lines changing depending on how the track is laid out. (Veteran kart racers shouldn't have a problem with this. Looking at the ASRT crowd.)
This post may change over time as I discover more. (As of posting this, I've only "speedran" the first 5 tracks of the 12. Posted a 4th, 1st, 4th, 4th, and am working a 16th up.)
Current Playlist of my PBs, including (as of this post) a 1st on track 2:
