You get Hm 08 rock climb from Professor oak after getting all 16 bagdes
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You can find some in the north of Cianwood City, just use Rock Smash on the rocks there and you might find a Heart Scale!!
You can smash rocks randomly to try to get one. If you don't want to go through trial and error, you can earn 1000 points in the Pokeathlon and trade them for a Heart Scale.
Mt. Mortar or you can buy it in the Pokeatholon Dome
Heart Scales can be purchased in the Pokeathlon shop for 1000P
first go to Mr. Pokemon first have the red scale and he will give you it