The second level is Swamp Palace, but we're both thinking of the first level which is Parapa Palace on the northern edge of Parapa Desert. I think a lot of people used to think that was Death Mountain, even I used to.
Death Mountain is north of Hyrule proper (where it should be) and in Zelda II consists of a series of caves. Take a look at the FAQ list for in-game pictures. The ultimate goal of Death Mountain is to get to Spectacle Rock. So I was wrong too in thinking that Spectacle Rock might be Parapa Palace and separate from Death Mountain.