It's specifically "six hundred threescore six" that you're thinking of; 66 isn't anything special. It's also Yian Garuga that's the wake-up call boss.
"Oh ha, it's an evil-looking recolor of that silly chicken from a couple ranks ago. This should be easy." *a few minutes later* "Where did all of my antidotes go?" (Seriously Garuga is the only time I've ever run out of status healers. I now bring immunities when I can.)
YKK's the Wake-up Call because he's the first legit Wyvern you face. By the time you face him you've gotten used to the small monsters and the chump-change Greats. You've gotten used to the easy telegraphs they make before doing just about anything.
Then comes the YKK quest. You come expecting the giant dumb chicken, and you find yourself in the actual tutorial for most of the rest of the game. A ball of random violence that you actually need to watch in order to find its tells, otherwise you'll get batted around like nobody's business. None of the baby toy starter weapons you've not really bothered to upgrade are any real use against it, and the sudden introduction of its rage mode just make it even worse.
It's no 666, because there are far worse monsters out there, but it does deserve a place in the 6s, even if it's just an honourable mention.