By Matti 9 days ago (Patch 3.3.0)
My raid group just completed this achievement and, strangely enough, we did not have to clear the whole instance.
The order we used was Razuvious -> Sapphiron and Kel'thuzad -> abomination wing -> plague wing -> Gothik and the 4 Horsemen. After killing the 4 Horsemen, we all got our Immortal achievement, despite not having killed any bosses in the spider wing.
I don't know if this means that the spider wing is no longer required for the achievement, or even that you can get the achievement by just killing the 4 Horsemen. I just thought it might be worth pointing out in case someone wants to try this (although if the former is true, then that's not much help, since the spider wing is unlikely to be a problem if you can clear the other wings with no deaths)