A godly Dragoon would have several gear swap sets. He would have the absolute best gear for each slot. To actually be godly, he'd even have to have his Relic and Mythic weapons. He'd have to have Relic and Mythic gear builds to complement these weapons as well. He'd have to have the Relic body armor because there are few other ways to augment a DRG's pet.
A godly Dragoon, additionally, would need to have dangerous solos recorded and posted on a YouTube account. DRG is very much about solo. This would show his skill and dedication to the class. Having street cred is essential to being considered godly.
Obviously, he'd have to have capped merits, but additionally, he should have nearly every job leveled to 37 so he can have the best possibly support job for any situation. Versatility would also be had by having him have all of his weapon skills capped, such as Staff and Sword.
One last thing, he'd have to do new research into the class and come up with never before seen facts. He'd have to publish these and gain notoriety as a well known brain on the topic of DRG and FFXI as a whole.
If a player did this, it would be hard to consider him anything but godly.