On the third island, Tan Line Island, start by getting the password to the temple.
Once inside the temple, this is a stealth section without any items. Move behind the hulking enemies, or they'll throw you back into the starting room. For the most part, this is straightforward. The only non-intuitive section is in the dark rooms; if you're in front of a window and Shantae is shaded, they won't see you.
Once past the majority of the stealth section, there will be platforming without items. Note that while you're in the main hub, the normal sized NPCs do not trigger an alarm. Your goal here is to ransack every room, looking for three keys. Once you do, go to the main hub and unlock the rooms in the top left, top right, and middle right to rescue your inadvertent allies. Exit the hub to the bottom right for a bunch of scenes, culminating in the Golden Pickaxe.