Grab as many Lums as you can
There are plenty of cute little bugs called Lums that you can catch on your runs. It isn't necessary, but try to catch as many as possible. If you can, try and catch them all. For one, it's just kind of fun to try and collect them. The other thing is, if you manage to do so, you will be rewarded for your efforts.
You will get an item that will allow you to give Rayman or one of the other characters some fresh new swag. The cool thing is, you can very quickly restart each level in the middle of your run. So if you just missed a bug by a hair, then you can get a fresh start without loading times.
Just keep in mind that, since this is an endless runner, you can't go backward and grab the Lums. You only can run forward so you have one shot to grab them. Just be aware, and you'll be a bug catching master.
Feel free to play a level more than once
Most levels in Rayman Mini will almost automatically make you play them multiple times. That's because when you first go through, you're coming in blind. So more than likely you will miss some of the items as you plow on. It's not a necessity to do so, but it can help you achieve a greater score.
In many games, familiarity plays a big role in success. Getting comfortable with the setting and surroundings will be beneficial. It'll make things a lot easier when collecting items. If you get familiar with the locations of the items, then it will be a breeze. And as I mentioned, don't be afraid to restart in the middle of the run if you aren't satisfied early on.
Try to attack often
You don't need to be out of control with it and overdo it, but having the finger on the trigger is a good idea. That's because you may need to use your attack to enable you to create new paths for you to advance on. This is especially critical in Challenge runs.
In those particular games, you are being chased by some kind of glowing wall that will end your run if it catches you. So it's important to think fast in certain spots and know that you may have to attack something in order to move on.
This will certainly come in handy in your normal runs too. This especially when coming across evasive items that will try to get out of your reach. So feel free to keep one hand on the attack button; just remember that you have quite a bit of jumping to do also.
Take advantage of the glide feature
In Rayman Mini, you have the ability to glide by holding down on the screen after jumping. This is nifty, especially for Challenges. There are times where a regular jump will do the job, but on other occasions, you'll need to glide.
I for one have foolishly tried jumping over a gap that I thought was jumpable only to find out that you needed to glide. So definitely keep this in mind when you see certain jumping opportunities. Heck, I'd almost use every time to be on the safe side, but if you're on a speed run, then it's better to balance things out.
It can slow you down a tad, but it really comes in handy. Plus, it's just fun to use, as Rayman uses his signature helicopter hair to make the move. You can't have a good platformer without some jumping, and the glide feature really adds to that element.