Ok, first and foremost, there are few skill challenge events per se, they are usually associated with other events and represent additional goals or challenges to meet.
During those events, you will need to do a certain numbers of skill uses, such as inflict specific debuffs on enemies, or use specific damage types on specific bosses.
The first and most important aspect of these is to read carefully the challenges that are given, because many skills or effects are similar, but slightly different. HP drain is not Max HP down, which is not Lifesteal…
Second, finding the right toons for this particular skill/effect. You can use lotbgamer site’s roster function to find which of your toons does which specific skills. You can also lookup those skills in the various guides published (Anthony Horton’s from the gamer group is regularly updated, the forum ones not so much).
For some effects, you can also find specific talisman sets that give the effect or enhance it (ie : explosives for burns, mark talismans, etc.).
Finally it’s time to put all this to the test. Build your team and go play to inflict those effects and rake the rewards in.
A few remarks that can optimize this phase :
Manual play is longer but allows more control, and thus may allow you to apply effects much more efficiently.
If using autoplay, remember the first toons to act get to consume the power points, so if you need to trigger a power skill, place your toons accordingly.
So it seems evident but needs to be said : if you’re planning on using autoplay, prefer toons that have the effect in their basic skills, as those will proc more often than power or fury skills.
Most skill challenges don’t care about the difficulty, this can allow you to use unmaxed toons, so be smart.
In the same vein, using a lower difficulty also saves sands of time, and is quicker to run.
You have a set period to do these, don’t try to handle all of them at the same time, make plans and you’ll manage to do those while also playing your troopers.