To unlock or "earn" badges, the text, spelling, punctuation, capitalization and everything needs to match what he sees on the screencapped instructions below the video tutorial. In the first 'Write Your Mod" badge, for example, the text in the green block needs to say: Hello, World! just like that.
Then the badge will unlock.
On the next badge, he should press the orange load start code button on the badge instructions. That will import the code he wrote in the previous badge. Then he'll scroll to the bottom of the badge instructions and select the correct quiz answer.
Hopefully that helps, but let me know if he's still stuck.