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Relentlessly Good Looking
Collect any class armor set from PvP Season 7.
Relentlessly Good Looking requires you to collect any complete class armor set from PvP Season 7 (Relentless Gladiator), which you can do by purchasing either the full ensemble or individual pieces from vendor Zom Bocom in Old Dalaran, Northrend.
Choose ensemble or individual pieces
The 
Ensemble: Relentless Gladiator's Ringmail Armor (example) costs 12x 
Mark of Honor from Zom Bocom in Old Dalaran, Northrend, while buying all 8 individual pieces costs a total of 17x Mark of Honor — so if you have no pieces yet, the ensemble is the cheaper option.
Buy ensemble for guaranteed achievement
Using an ensemble immediately grants the achievement upon applying it; if you buy individual pieces instead and the ensemble shows 'already known' without the achievement triggering, you must refund those pieces and purchase the ensemble directly — owning all individual pieces does not award the achievement.
Clear any active trade timer
If you purchased the final piece but the achievement did not trigger, the item may have an active refund timer preventing it from being added to your collection; deleting the item, disenchanting it, placing it in Void Storage, or selling it to a vendor for gold will immediately clear the timer and grant the achievement.
Tips
No old PvP rank is required to purchase any Season 7 items from Zom Bocom.
If you only need a few pieces, purchasing the full ensemble may still be cheaper (12x Mark of Honor) than buying 3 or more individual pieces at their combined cost.