Your character needs to be an adult, and you need to have the mirror.
The mirror is sometimes available in the shop in your Tamagotchi. If you don't see it there right now, check back in about 4-6 hours*. You may not see it for a couple of days, but eventually one will show up. You can use the time to get Gotchi points because you'll need them, since the mirror is expensive (4300 Gotchi points if I remember correctly).
* Note: shop restock times are 3:00 PM, 7:00 PM, and 12:00 AM (midnight)