Grandmaster 1 & C

The most significant time saves of these runs are the dismount and remount of Yoshi at 0:35 and 2:48. This game lets you maintain full lateral speed in the air for only about 10 seconds. This imposes a limit on the distance infinite flutter can travel quickly, but there are a few ways to reset this timer: dismounting from Yoshi, remounting Yoshi, and doing another head shake all reset this timer and allow Yoshi to efficiently infinite flutter from the 2nd section to the Launch Star at the end of the 3rd section. This not only skips most of those 2 sections, but it also allows us to keep Yoshi and use infinite flutter to the end of the level.
I use Mario for both Stars because he can long-jump about 7 frames earlier than Luigi, and Mario's long-jump is fast enough that he doesn't lose time during just 1 long-jump. Luigi moves slightly faster backwards after dismounting Yoshi, but as far as I can tell, this provides only a couple frames of advantage.
The Ultimate Test - 1:46.98
When starting a backwards flutter, Yoshi can move faster if he head-shakes and starts fluttering as close to the ground as possible. This only slightly saves time during the first couple flutters of this Star, but it becomes important in the next section.
0:27 - It's critical to get as much speed as possible during the backwards flutter away from the 2nd section. Without the speed increase from the low backwards flutter, Yoshi will lose almost all speed during the sideways infinite flutter before reaching the next Launch Star. With the increased speed, the backwards flutters can be ended early at 8 flutters and still allow the sideways flutters to reach the next Launch Star before stopping.
0:34 - Just before dismounting Yoshi, I release the analog stick for about a second to slow down. Dismounting at full speed requires further delaying the ground-pound in order to remount Yoshi, and that loses too much height to reach the Launch Star.
After remounting Yoshi, I turn left, do a midair jump, and start a sideways infinite flutter. To be able to turn left, it seems like the analog stick needs to be held downwards during the jump at the beginning of the backwards flutters. If the stick is neutral during the jump, holding left won't cause Yoshi to turn after the remount.
The midair jump always works as long as the A button is pressed with the correct timing. The timing window seems lenient, and it usually wasn't a problem during attempts.
1:40 - The Boomerang Bros. can be defeated extremely quickly with Yoshi's tongue and 2P, as shown by PurpleSun's TAS: • [TAS Demo] SMG2: The P... . In retrospect, hitting each Boomerang Bros. with Yoshi's tongue and then bouncing on each even without 2P would have been about 0.2 seconds faster than what I did.
1:45 - The Star grab is about 7 frames late, but I got my goal time of 1:46 by 1 frame, so I settled for it :p
2:11 - The Perfect Run - 1:50.68
2:15 - The low backwards flutters save about 3 seconds over using the Flower Grapples in the 1st section of the Comet Star. I initially jump to the left and delay the head shake a bit to get more speed in the first 3 flutters. Trying to head shake as soon as possible usually gained less speed, but TAS precise execution could probably make it work better.
3:25 - I usually held up on the analog stick when bouncing off the Toad. However, sometimes I needed to hold very slightly left to avoid missing the next Launch Star to the right. It seemed like I needed to do this if the bounce on the Octopus at 3:17 was on the left half of its body.
3:55 - I was extremely lucky to not get hit by a boomerang after ground-pounding the last Boomerang Bros. I don't know if the boomerang's shadow is indicative of its hit box, but it looks like Mario is just barely to the left of it. I collect the sole Star Bit so I could shoot the incoming boomerang, but I completely forgot to shoot. (I likely would have missed anyway.)