From the description I'm thinking of a fairly young child, But I think this could apply to pre teens. Child may have problems being expressive in loud over stimulating places. It could be an on going slow process of one step forward two steps back. The "shy" child's friendships depend when able to spend time one-on-one with their friends, instead of in groups. The less boisterous setting makes it easier to express thoughts and respond faster in play time. "Ah, I've finally gotten over it!" but at day care/park/large play group once more struggles to keep up and feels stressed out.
After becoming use to and having stronger friendships with a group of 2-3 the child once more has built confidence and is able to keep up, or even lead group activities. Once more "I got this, why did I ever struggle?"
Either a new kid is introduced to the group, the shy child has to adapt to a new setting, or one of their closest friends is no longer around to help soften the struggles with group time. Possibly any combination of the 3. Panic, stress, and confusion takes over once more. Again, what was strange becomes familiar. Again adapting the child has new skills and confidence to express inner self.
From my personal experience, being "brave" was never really an issue. Feeling stupid or unwanted in a setting or with a group of people was. My anxiety was usually connected with not knowing what to do, but once I could focus on something and then expand into other areas I was fine. I also had a speech impediment that was a struggle at least to age 9. I avoided saying some words because I knew I'd get made fun of for saying them wrong. Having other kids around that didn't make fun of me helped me to feel more relaxed. For other children I know they had a lot of fears, so tackling those fears in order to be brave was an issue. Some kids I knew had a hard time being a away from their moms for very long. Others didn't like play group games like tag because they were scared of falling and getting hurt.
How to help the character become less shy really depends on why they are shy and how old they are. Some kids with ADHD or dyslexia have sensory overload problems. So they can be perfectly social at home and aren't actually shy, but in situations where it's loud with lots of distractions it's hard to think and they appear shy. Really, they are just trying to take everything in, but can't process fast enough to respond. Other kids are just strong introverts, they are fine they just don't want to be bothered. But people who don't know them assume the child is shy or has something wrong with them.