Mega Man Legacy Collection

If you die at any point, push the view button on your controller and select restart challenge.

From the main menu, select "Challenges" then scroll to challenge #4 "Mecha Dragon".
Once the level begins, you instantly want to start moving to your right using and tapping and holding to jump across to each block, once you can't see a block to land on, stay still and wait for one to appear before jumping or you will hit the side of the screen and fall to your death.
Once the level stops moving, you will then be faced with killing the Mecha Dragon. You want to jump up to the second block, fire using and when he fires his first flame, you want to jump this and continue firing on him. He will then blast a second big shot at you, in which you will need to jump to the top block in order to dodge, then continue firing. By now you should have already defeated him. If not, when he fires a 3rd shot, jump back down to the second block and start firing on him again.

Once defeated, you will have your bronze medal.

There's an easy way to see the optimal solution for any Challenge in the game: Select the challenge, and press to see the Leaderboard for that particular Challenge. Then you can simply select any high score and press to watch the Replay of that particular record run.