I just went from 0 PVP gear (not even previous tiers) to 4pc Grievous + Weapon + Trinkets and then the rest Tyranical. Thanks to the catch up CP option and JP > Honor I was able to do it in a couple nights
I went for this based on 0 pvp gear:
Head (pve meta useless) > Legs (2pc) > Trinkets > Weapon (now meet 7500 CP requirement) > Hands > Shoulders (4pc) and then farmed JP/HP for the rest in Tyranical. Will be able to get the Grievous chest this this week plus a 1250 item.