The second stage in the castle is blessedly short, like its companions, but that doesn't mean it's a walk in the park.
When you first appear, you'll be on collapsing ledges. You can climb these to the top portion of the screen, then climb up the ladder on either side. When you reach the top of the ladders, you can then drop down to collect special weapon refills if you desire, or you can just get on with the assault on the castle.
Once you're ready, work up the right side of the screen, until you see a thin ledge leading to a ladder on the screen's left side. Cross over to that ladder and climb up it. You'll now be facing a narrow sliding space, with green-colored tiles that indicate there are those steel traps you're familiar with from Hard Man's stage.
Slide through the opening and you're now looking over a field of spikes with trap-colored ledges leading across. Switch to shadow blades for this part, then hop quickly across the gaps. When you reach a fairly wide ledge between two traps, throw the shadow blade up at the bee that swoops in, so it's destroyed before it can attack. Then start hopping along more ledges that lead to the right. About two ledges in, there will be another of the bees, so be prepared to take it out with another shadow blade as you hop toward the right.
The next time you encounter a safe ledge, just right of the last of the green-colored traps, it's time to switch to the Rush Jet adaptor and, with that done, ride toward the right. Your jet can take you from one special item refill to the next, and you should soon come to solid ground in front of a gate leading to the area boss.
NEXT: Stage Three