However if you have recommended legendaries and are up for a bit more of a challenge you can attempt it at far lower item level, furthermore you can do at even ~890 without any of the recommended, but it will take a number of tries and solid execution. Generally I will recommend to have ~920 item level and 66 traits before you start it.
Learn more about other top things removed in 8.0, and if you've enjoyed learning new classes for the Mage Tower, check out how classes are changing in BFA.
When the pre-patch hits, the Mage Tower Challenge can't be completed, so you have limited time left. The Battle for Azeroth pre-expansion patch date is July 17th (US) / July 18th (EU).
