I agree with everyone about the manageable goals. You might make a list to check off so you feel good when it's done. Although, for me sometimes cleaning a bunch at once is easier than in small spurts because I get distracted and will never get it done if I don't just do it at once.

Perhaps do something you enjoy once you are done. I also listen to music or podcasts to keep me entertained while I clean because sometime it is just boring! Also, you could work on making a habit of putting stuff away as you go once you clean a section.

My apartment was terrible when I was really depressed this past year, I got it clean and once it is clean it is easier to just keep it that way if I maintain it. It is hard to get started, but I find it gives me momentum once I get going, because then it feels so nice to see it clean and it improves my mood. It even got me motivated to decorate a bit. I know it's tough, though, when you are depressed.