As the title says, I am working on Conquest 4 - Reach Greater Rift Level 55 Solo with the Full bonuses of six of the following class sets, on the Switch.
I was able to do the first three on my Crusader no problem. I switched to Barbarian and have run Immortal Kings, Raekor, and Might of the Earth, full 6 piece bonus, GR 55, several times each in the last two days. They are never updating that I have completed them.
I am aware that on PC there was a known issue that may have also been on consoles where credit is given but the check mark takes time to update, and it would still complete the Conquest if you did all 6. That is not the case here - it is simply stuck.