Reposting my advice from the other thread, with a couple of additional tips:
For high scores, you need to get to max combo (4 or more consecutive bonuses in a row) consistently, and you need to clear a lot of blocks while you have max combo.
This version of Lumines requires clearing only 3 squares to get a bonus, compared to 4 for every other version of Lumines. That's a huge difference in practice and will let you get bonuses much more easily.
You won't have enough time to get bonuses if you spend too much time rotating and sliding blocks. The key is to drop as many blocks as possible in one timeline sweep while still clearing squares and without overflowing yourself in the long run.
For skins with fast timelines like Shinin', a lot of the time you just need to get the bare minimum of 3 squares, then start setting up squares for the next timeline sweep before the current timeline sweep has finished.
The best way to learn this is probably just to force yourself to play without rotating. Drop every block as you get it, and try to figure out the best place to put it as close to the middle of the field as possible - you have more options than you think, especially if you "slice" the block effectively. (Time attack mode in the other games was very effective at forcing you to play this way.)
You need to get as many combos as possible early on, while mistakes don't matter as much. Later on you have to abandon this kind of high-risk playstyle because every mistake will cost you at higher speeds.
If you use an avatar that lets you stop the timeline, use it just before you get a max combo to give you enough time to set up a huge score bonus on the next sweep.
