Enter the first shop, where you'll automatically obtain the Rope Dart. Buy "Karuta plates" and "Serendipitous bodies." This is necessary later for a laser skip in the Tower of Time.
For the beginner strat, hold right to avoid taking damage from the fire kappa.
Ropedart climbing is optional for the beginner strat, but without it it's harder to ropedart the middle stalactite, so usually the platforms are just jumped across to ropedart the leftmost stalactite.
Doing the kick beginning of the advanced strat is optional. You can also ropedart the stalactite instead of the lantern at the end.
You can either ropedart or slash the green kappa on transition, the distinction is mostly due to preference for what makes getting up to the ledge easier.