From Fallen London Wiki (Staging)

Getting this destiny ought to have an actual dedicated guide on <a href="/wiki/Irem_(Guide)" title="Irem (Guide)">Irem (Guide)</a>, as the only thing recorded as of right now is the path to get there. It just seems a bit counterintuitive to lead people on the correct path only for them to reach it and be blocked because the wiki just didn't say anything about it. There's gotta be a good path for this so it's not as messy to get.

Edit: From what I can tell, the best path is to go from Nearby to Abyssal to Dark, back to Abyssal to Altered, back to Abyssal and back to Dark to No Future. Stupidly complicated, but it gets you the items you need before taking you to the end goal.

Edit 2: So I am just dumb, I completely forgot about the need to get to A Brilliant Future for the Memory of Sunlight, which completely invalidates that neat little back-and-forth