There's not much to say about this TAS. It's a very simple platformer split into 60 levels. There's no reason to go over each level, just a few tips and information.
Lag: This game has a lot of lag. I do some movement to minimize it, but as far as I know, the control the player has over lag is quite minimal. There are some things that always cause lag though, and should therefore be avoided. Touching a flower always causes lag, and activating the snowflake shaped platforms that launch Olaf up often cause lag. Most lag comes from the many unavoidable collectible items, or spontaneously.
Slopes: Running on slopes, up or down, is slower than on flat ground or in the air. I didn't realize this until level 16, so on level 7, 11, and 13 some time is lost on the slopes. (Also going back through the TAS I seemed to totally blank on it at the end of 18.) Most of the time on long slopes, I will jump whenever I touch it to stay in the air. Keep in mind that on level 28 I'm forced to stay on the slopes to avoid entering the wind gusts.
Air movement: Olaf gets one grounded jump, a midair jump, and then the ability to hover midair for a short amount of time with reduced horizontal movement speed. This has to be used a lot, but because of the reduced speed it is minimized as much as possible.
Ground pound cancel: Ground pounds must be used in a few areas to break ice blocks. The ending animation for this loses time, but you can cancel it by throwing Olaf's head on the same frame the block breaks. It breaks the block, ends the ground pound, and immediately ends the head throw.
10th levels: Every 10 levels is an autoscroller where you have to escape a threat from the left. If you die though, you can still move on to the next level, and this is much faster.
Credits go to SnessFresh for most of the strats and knowledge taken from his world record run, which can be seen here https://www.youtube.com/watch?v=9VOHJ5kbXas&t=588s
Thanks, God Bless.