I can do well in pretty much every single event except for this kind of event, yet there are loads of people with rank 2 mythical dragons that are only obtainable through these events. Are there any tricks for getting the most value out of your moves or something?

Most of the hacked dragons in the game are dragons that were available in the match-three puzzles. Not all of the ones you are seeing are legit. I think everyone hates match-three events equally, lol. The only tips I have are to focus on the pieces for the dragons you want, don't go out of your way to make a five-match unless it's going to help you get the dragons. Also try to use your power-ups before the puzzle level resets or it might get lost!