You don't need a certificate. But you might be required to show proof of how much you've helped out on SE, for which these statistics might be useful (please see @animuson's caveat below):
Note that unless you've answered questions that were newly posted, the "people reached" statistic isn't really helpful (you can post answers to old questions and have the stat shoot up without actually having reached out to all those people).
You'll be helping the community in a way that they learn something from your answers provided they are of good quality. Answers which are helpful to the community will be upvoted.
You can also earn various badges on sites you've participated in. You currently have 8 badges on Meta SE.
"You've spent this much time here and answered X questions"
There's a calendar in your profile (that is only shown to you) which you can use to see how many days you've spent on each site.
You can answer a few questions every day. This would reflect on your profile page along with the specific date and time of answering:
The calendar can be used to verify whether you've answered any question(s) on a specific day (by cross-checking the dates in the Answers subtab) or if you've just simply visited the site.
At the end, you could share a few screenshots of items that are only visible to you (such as the calendar) and a link to your profile page with your facilitator.
If your school does require a certificate, then there's nothing that can be done from SE's side.