It looks like it was a typo and you meant "crystal" in which case, once you get to blackthorn city and defeat Claire, you must go to the dragons den which is a short surf behind the gym. Once inside surf down and to the left until you see a whirlpool. Use whirlpool and keep going until you get to a building. Go inside and talk to the man at the back of the room. If you answer his questions correctly, Claire will walk up and give you the 8th badge.
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The HM waterfall is in the ice cave, the cave you use to get to Blackthorn City to get the 8th badge. Just pick up every item that you can see in there and you will find it.
You have to beat the gym leader, Pryce, in Mahogany City.
You can obtain the 8th gym badge (the earth badge) in fire red from Giovanni in Viridian City.
I'm pretty sure it should be the last badge before you go off to the elite 4:)
in Viridian city. the one that was locked.