Well you should be used to the basics of match-3 games by now, but just in case you're unfamiliar: you want really big chains in order to make quick progress. And yes, connecting many icons together at once will help.
You only need three icons to be matched in a match-3 game, duh, but if you match 4, 5, or even more depending on the layout, then they will combine into super icons. Bombs, rockets, and explosive disco balls which can change the game entirely, and save your ass.
The best practice is to use rockets and bombs tactically, attempt to combine special icons if you can, and if you're stuck focus your matching efforts at the bottom of the screen in hopes that will shake up the upper layers.
The main "story" of The Short Timer Strikes Back is that Retsuko is helping with the office relocation, which is great, but she must do most of the work herself. Typical.
By clearing through puzzle stages you'll earn stars, and you can get up to three stars for each puzzle, depending on your score at the end.
Stars will be used to improve your office, giving you more furniture to play with and you will eventually find yourself moving up to decorate further floors of the office building. Your goal lays right at the top.
The ideal hero
One interesting change to the typical match-3 formula is that, in a weird way, Aggretsuko: The Short Timer Strikes Back is also a gacha game.
Yes, you'll be collecting characters from the Aggretsuko universe, and each of them will have a unique special ability which you can use to help crush blocks and tear through the more difficult stages.
At the beginning of each stage you'll be allowed to select a character, you should often choose whomever is recommended, and more characters will mean better odds.
Well, now we need more characters, don't we? As you first start up the game and clear through the initial missions and achievements you'll be rewarded with a few draw tickets, and a lot of gold.
You can use your draw tickets to quickly summon characters, and then once you've run out you'll be spending 50k gold for each draw. It's nice that gold is easy to get in this game, at least at first.
Another thing that's nice is that there are no character tiers of rarity, so they all have the same draw chance. It's not nice that you'll likely get many duplicates before completing your collection.