First the child -- are they shy, do they do well in large events? Key everything off the answer to those questions and you can't go wrong.
Second, make sure as you plan your party that you as the parent have the ability to step away from running your party (recruit friends to help take pictures, refill snack bowls and serve food to guests) and be WITH your child during the performance.
Many parents forget that their child wants one thing and one thing only at this age (3-9 yrs) and they want the gift of their parent's Presence when they go through this event of meeting their heros. They want mom or dad to sing along with them, put on a tiara and hold their hand when they can't stand still because ELSA is there!
Third, make sure there is enough space at your event for the entertainer to entertain. If you have a Superhero training Academy, then you should look for at least a 10x10 space free of tables and "knockoverable" things or a spot in your backyard (weather permitting) where you can set up a training course.
Fourth, know the weather and have a fallback area inside your house or at a venue so if the weather changes your party can continue.
Fifth, If you have a crowded party (bounce house, pool, pony ride, etc) to get the full value out of the performance, unplug the bounce house or temporarily halt the other events going on during the performance if possible. There is nothing more disappointing in a home video of having the whine of the bounce house fan distract the viewers from the premium singing performance.
Sixth, consider the age range of your guests and provide appropriate guidance. Sometimes those children under the age of 2 - not the party child - are not able to partake in the event without disrupting it. It is best that the parents of those children be nearby so they can be called on to resolve the situation and maintain a fun atmosphere for all.
Finally, if you are having a mixed party of children and adults, as usually happens when you are having a family party at the house, consider carefully what happens during your child's performance. If you have all the parents congregating in the kitchen, that is where the children will want to be as well! If you leave the kids with the party entertainer while all their other family members are drinking, socializing or eating, sooner or later all will slip away and you end up paying the entertainer to be a babysitter.