To get more Brawlers, all you need to do is play the game! They are obtainable from pretty much everywhere, so with patience and a bit of luck, it's a matter of time until you add a new one to your collection.
Unlocking all the Brawlers is a combination of luck and a bit of patience. This is by design, and is how we make progress fairer for everyone.
Here's where you can find them:
Once you reach the required amount of trophies, you get to keep them forever!
Using "secret codes" to get Brawlers or similarly asking through Player Support will not work. Similarly, it won't improve your chances of unlocking Brawlers from boxes. The only ways to get brawlers are those mentioned above.
Legendary Brawlers are not stronger than the rest of the rarities!
If you have not opened a Legendary Brawler, though, it might be a blessing in disguise. The road to master includes your current Brawlers, and as you practice with them, you will be able to open more boxes and eventually find your way to a Legendary Brawler. Patience is a virtue!