Note that the shield cant be shooted if the dragon is too close.
Thats the reason it'll atack your sword.
You have to keep your shield close to dragon, but not follow him. Then when dragon atack your shield come closer with your sword. If dragon start to kill sword move back and repeat. Still this badge is really hard. Should be impossible IMO
Just a quick tip: here is the Step-by-Step tutorial for all badges:
http://www.kongregate.com/forums/22-elements/topics/134611-updated-v1-26-step-by-step-walkthrough-to-getting-the-elements-badges
BUT dont kill the 3rd leveled computer till 500 points fight versus player, it'll grant you the third badge and 500 points faster!
TIP for ultimate cash:
1.save the game
2.go gambling, bet all your cash on fighting lama (no matter which)
3. if you lose, load the game
4. If you win, save the game and play again. Note that the maximum amount to gamble is 400, so you can buy cheerleaders and equipment up on.
5. repeat till almost dead
6. 99999999999999999999999999999999999999 cash