As qwertysaur mentioned, Barbiriccia and Rubicante are variations of the don't attack boss in FFIV.

In FFV the Sandworm uses a similar tactic since it hides in the holes and you're meant to wait to attack it unless you want a gravity to the face. Siren can also be seen as a variation since she switches from Undead and alive and messes with her strengths and weaknesses.

For FFVI, ignoring the reskin version of Ymir fought in the Dragon's Den, the only boss that pulls a variation of this strategy is Chadarnook (the painting boss) as only the demon form can truly be killed and attacking its goddess form has it throw some nasty counters your way.

Also Heckran uses this strategy in Chrono Trigger though unlike the later FF variants, no one warns you he has a mean counter attack. Likewise Kahran Ramsus has his Mirror Stance in Xenogears that works on the same principle. So SE used it in other non-FF related games as well.

So yeah there are a few bosses who have similar if altered variations of the starter boss strategy but like has been mentioned by Karifean, the whole point is really to teach people how ATB really works compared to typical turn based.