There's no "fast" way to fight the 500 battles needed, but joining popular farming bosses can cut down the time you spend waiting.
The most popular boss by far is Loremaster. Waits for her are often ten seconds or less, especially if you farm her in the evening.
If you're using team-up to help with any other battles, however, please be sure to actually help the wizard who requested a team. Be sure they make it into the battle ring before the boss is killed. Take out the minion for them, help them set up a hit, heal them if you can.
There's not really any method. The only thing that would make it quicker is to simply avoid big dungeons with multiple bosses. Wizard City bosses are obviously the easiest to defeat so you're best working on that and Krokotopia.
Congratulations on working towards the Team Leader Badge; you shall earn this, get the Blaze Fox; and even more!
You already know you have to help teams to earn the badge, but how to do this faster?
Do some research, and find out what the fastest battles and dungeons are in the game, then simply continue to reenter those battles and dungeons, via the Team Up Kiosk outside the Bazaar.
I like to do the Loremaster Dungeon, because battles are over in seconds and minutes, and Loremaster drops spells, and treasure cards. Team Badges
Team Player Badge - Help 100 Teams Team Leader Badge - Help 500 Teams; this badge allows a player to buy the Blaze Fox Pet, from the Team Up Vendor outside the Bazaar Team Manager Badge - Help 1000 Teams; this badge allows a player to buy the Sand Storm Mount, from the Team Up Vendor outside the Bazaar Team Champion Badge - Help 2000 Teams