Since it's the most difficult feat the game recognizes, I took my permadeath character to the end of the Atlas Rises storyline today. Unlike my survival Gek I condemned this Vykeen to the incredibly hostile Calypso galaxy, where every day will be a fight for survival.
Sure enough I awoke on a world blasted by radiation storms and made it to my ship only by digging tunnels. Made camp on the 1st non-murderworld I came to, an eerie glitch I named Cliffhanger Ending, and called the story complete.
Still playing NMS off and on. Lately I've been playing less of No Man's Sky The Infinitely Large Place To Wander Around In and more of No Man's Sky The Videogame - finding a good S-class multitool and ship, grinding to become fluent in Gek, making various numbers go up. It's an okay way to relax in the evening.
I did build a couple of new bases in some interesting places. This "mega exotic" I named Hercules Monochrome, after its distinctive atmosphere: