I know a lot of Final Fantasy games have had optional side bosses that were quite a feat to defeat. Does Final Fantasy 13-2 have anything similar?
It doesn't seem like there are any mega bosses that pose a serious challenge for fully maxed-out players. Raspatil's lack of Doom/Wound damage can easily be exploited by having a Sentinel out, and his strongest attack can be blocked with the Tortoise paradigm (SEN/SEN/SEN), allowing even under-leveled players to emerge victorious with a fairly simple strategy. Fully-leveled players will be able to achieve a five star rank on this battle (among other supposed "mega bosses") without needing to employ unique strategies like those that were needed to defeat/five star the Long Gui, Vercingetorix, Neochu, and Gigantaur in FF13 (the four hardest bosses in my opinion, and all harder than any boss that exists in 13-2).
Ironically despite that the advertisements for the game talked about how Wound damage would increase the level of strategy needed to beat the bosses and stronger enemies (so you couldn't just spam Sentinels/Medics), the game's battles have less of a sense of urgency than in 13, where many of the bosses casted DOOM.
Sadly the grading system in 13-2 rewards players for having a higher level instead of taking the enemy down with the most effective strategy. In 13 target times were adjusted according to your stats, which meant it was possible to five-star an enemy if you were severely under-leveled as long as you were strategic in your approach. In 13-2 the target time always remains the same - so essentially the game prizes players who spend more TIME playing the game instead of players who IMPROVE their skill.
The most strategy-inducing battle in 13-2 is probably Yomi, who unfortunately is just an easier version of Vercingetorix from 13. Against Vercingetorix, even fully-maxed out players can have difficulty, especially if going for a five-star ranking. The poison strategy requires actual manual ability selection, a quick-fingered switch to SEN/SEN/SEN to reduce damage from Wicked Whirl, and a good setup beforehand. If you want mega bosses, play 13 - the Neochu, Gigantaur, Vercingetorix, and Long Gui fights will be much more satisfying than any battles in 13-2 when looking for a challenge.
Yes Final Fantasy 13-2 has something similar.
On the archlyte steppe there are 4 mini-bosses namely
You can get the quests to defeat these monsters from Myta and the hunter outside the chocobo camp.
There is also a mini-boss in Oerba-400AF called Raspatil and it is one of the strongest mini-bosses in my opinion.
Then there are also different endings you can get by beating bosses while the paradox scope is active. Engaging these bosses with it active increases their stats significantly.
In addition, the Coliseum is meant to be a house for optional encounters released as DLC: