When playing slots, eventually a Clefairy will appear. I'm not sure what triggers it. Next you need to get a 777. I'm not sure if there is a time limit to do so, but I can't rember ever failing to do so. Now the Clefairy mini-game starts.
I don't know if this is the best method, or why it works. But I've managed to reach round 10 twice with it. It doesn't always work. You'll need to try several times.
Basically follow the Clefairy's directions. When it points left, hit Y. When it points up, hit B. When it points right, hit A. You'll win 15 coins. If the Moon glows red, intentionally choose to stop the wrong one each time. If the Moon glows white, continue as normal. The White moon probably means something, but I don't know what.
If you are lucky, you'll last until round 10. I don't know if you get Explosion for reaching Round 10 or beating Round 10. Just keep going as long as you can.
You can only get one Explosion TM. Getting to Round 10 again will not let you get another one.