Ooh, tough one. I struggle with top 20 lists generally, and as far as contemporary-ish artists I love go, I reckon the Mountain Goats, Fucked Up, Lana Del Rey, Death Grips, probably Ramshackle Glory/Pat the Bunny and arguably Xiu Xiu all did their best work before 2013. But Dose Your Dreams, Ultraviolence, Government Plates, Possibly Nothing, Probably Everything, Angel Guts and Forget are all pretty respectable entries. Beach House, Protomartyr, Run the Jewels and Waxahatchee have all had strings of amazing albums within the last ten years. And Iceage as well. It's the Big Joyous Celebration, Let's Stir the Honeypot by Teen Suicide and Take It, It's Yours by Katy Goodman and Greta Morgan/Salpeter come to mind as two I really loved. And New Alhambra by Elvis Depressedly. And looking for albums from 2013, that was the year that Earl did Doris, Hard Skin did Why Do Birds Suddenly Appear?, Kanye did Yeezus, and MIA did Matangi, unless my music player is lying to me, which it sometimes does.
Tl;dr I am terrible at making top 20 lists and have no idea what my top 20 albums are, but there's a lot of decent albums from the last decade that could well be on there, especially by Beach House and Protomartyr/