What HMs are required to beat Heart Gold after Jasmine's gym?
Hope I helped!
Cut (HM01) for the tree outside of Erika's gym
(Catch the Farfetch'd in the Ilex Forest)
Surf (HM03) for the Dragon's Den and getting to Kanto through Tohjo Falls
(Defeat the Team Rocket Grunt in the Ecruteak Dance Theater)
Strength (HM04) for the Ice Path and Victory Road
(Bump into the Hiker outside of Mt. Mortar/Ecruteak City)
Whirlpool (HM05) for the Dragon's Den and getting Lugia in the Whirl Islands in the postgame
(Clear the Team Rocket Hideout in Mahogany Town)
Waterfall (HM07) for Tohjo Falls
(Item on the floor in the Ice Path)
Rock Climb (HM08) for Mt. Silver
(Obtain all 16 badges)