Link's Twilight Costume is unlocked by achieving "A" Rank as Link on square G-4 of the Twilight Map. This is a double run of the stage, first to unlock the costume and obtain the first Skulltula, then the second Skulltula.
Unfortunately, the Heart Piece eluded me on this one. Turns out I confused a keep that was captured using the Magic Circle with one I controlled from the start. The Heart Piece is obtained (not shown in either run) by capturing the first keep to the northeast of the Enemy Base.
Voice commentary is on and audible in this video.