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The left path is definitely the trickiest! Here's a full walkthrough:

• Starting at the looming gate, go right, then down. Then go left until you can't anymore. Then go down until you can't anymore. You should be in a room with a purple background and see Diggur.
• Diggur is looking for the purple key, which you can see. If you walk to the right and come back around, the key will be gone. Diggur will have left a note saying that he's gone to dig past the door. If you visit him, you can see he's partway through digging the next room.
• Go back all the way to the right, and drop down the pit at the bottom of the screen. This will loop you back to the room you're currently in. To get past this, you'll need to hold left while falling to land on the ledge and go into a secret passage.
• Keep moving through to the left, collecting the purple key on the way, and eventually getting to the other side of the purple door. 
• At this point, Diggur has finished digging his tunnel, and you can follow him to the other side and talk with him again.
• If you continue past Diggur, you'll see a ledge that's too tall for you to jump up. To get to the top of this ledge, you'll need to return to the room Diggur is in, jump up the platforms to the room above, jump to the top-left platform, and jump off of it while holding left. This should give you enough height to make it to the top of the ledge.
• Continue left and you'll find your way blocked by an invisible block. You can jump onto it, and subsequently the block above it. Then, jump into the room above. This room is a zig-zag pattern of invisible blocks. Once you make it to the top-right, you can jump up to the next room, which contains the Orb of Caverns.