Fundus photography has routinely been used to document the presence and severity of retinal degenerative diseases such as age-related macular degeneration (AMD), glaucoma, and diabetic retinopathy (DR) in clinical practice, for which the fovea and optic disc (OD) are important retinal landmarks. However, the occurrence of lesions, drusen, and other retinal abnormalities during retinal degeneration severely complicates automatic landmark detection and segmentation. Here we propose HBA-U-Net: a U-Net backbone enriched with hierarchical bottleneck attention. The network consists of a novel bottleneck attention block that combines and refines self-attention, channel attention, and relative-position attention to highlight retinal abnormalities that may be important for fovea and OD segmentation in the degenerated retina. HBA-U-Net achieved state-of-the-art results on fovea detection across datasets and eye conditions (ADAM: Euclidean Distance (ED) of 25.4 pixels, REFUGE: 32.5 pixels, IDRiD: 32.1 pixels), on OD segmentation for AMD (ADAM: Dice Coefficient (DC) of 0.947), and on OD detection for DR (IDRiD: ED of 20.5 pixels). Our results suggest that HBA-U-Net may be well suited for landmark detection in the presence of a variety of retinal degenerative diseases.