I know what you thinking, that guy has already done that as a pub crawl (I know, Sam Cullen,
https://innsidetrack.wordpress.com), but what difference should that make? I'm also thinking of expanding it slightly by also including stations that are still open that were once, but are no longer, Underground stations. The former East London Line, which is now part of Overground, for instance.
Having done the Labyrinth Challenge, I can now say that I have either stepped onto or stepped off of (often both) a train at all 270 Underground stations. But often, if the Labyrinth was on the platform or anywhere else inside the ticket barriers, I didn't actually see much of the station. Even if the Labyrinth was in the ticket hall, so I had to exit the barriers and re-enter, I didn't leave the station property, except when I had to walk or catch a bus to the next one. So, this time, I'm going to take my time, leave the station and have a proper look around.
I'm going to buy a new Oyster card, which I will use only for this project, which I will call the "Chronoyster". When I request a journey history, that will be the log of my travels.
So I start with my first 7 stations, by going back to 10 January 1863...