In both Paper Mario and Bug Fables, an important battle mechanic was
that certain enemies could be flipped over onto their backs when hit by certain
attacks. These were usually enemies with notable Defense Power, and flipping would expose their
soft underbellies, dropping their Defense to 0 while flipped, or at least to a
smaller number than normal. Depending on the enemy, it could also need to spend one or more turns
getting back up, giving flipping the additional benefit of temporarily
preventing the enemy from attacking. In PM, enemies that could be flipped were usually Koopas and
other creatures with similar shells, while in Bug Fables it was less clear-cut,
and flipped enemies could always right themselves as soon as their turn came back around and
could even attack in that same turn. Furthermore, enemies in PM were flipped by jump-type attacks
as well as a few others like Quake Hammer (and in the second game, Clefts were instead flipped by
explosions), whereas in BF it's primarily Kabbu's horn that flips things, along with a few other
Arpeggio, by default, excludes the flipping mechanic because I don't want players to feel restricted in the types of attacks that they can design, nor Maestri in the types of enemies, as it's a trait pretty specific to Mario and Bug Fables creatures. Instead, I made Koopa Shells count as a form of armor, allowing player characters to potentially steal and wear the shells themselves (I've always loved the Blue Shell power-up in NSMB). That being said, it is not overly complicated to add flipping back in to a given Arpeggiated game; you could even make it so that anyone who's wearing a Koopa Shell could be flipped, making it suddenly more risky to use them as your own armor.
If the default is to exclude flipping, the default when not defaulting (i.e. the default way to add flipping back in) is to take the Bug Fables route and assume that anyone who's been flipped over can get back up as soon as their Phase of the turn comes around again, and doing so will not use up their turn. This simplifies things and makes flippability less of a major weakness. It's also fine to make getting up use up a turn, but in Paper Mario, it often took some enemies multiple turns to get back up, with this turn count being refreshed any time that they were hit by another flipping attack, making them easy pickings even in groups. If you want to replicate this, feel free, but you'll have to decide how to determine the number of turns that it takes. Going on a per-enemy basis would require indicating the number on the enemy's sheet, which you won't see me doing. You could instead use a field stat, like Hand-Eye or Platform, which would make some kind of sense, but I assigned these stats without this system in mind.
What types of attacks are capable of flipping targets over can vary between different games of Arpeggio, but the default types include anything resembling a jump on top of the head (or on the back if the target is quadrupedal), earthquakes of any kind (which tend to be multitarget, so would flip anyone who can be), or anything resembling Kabbu's basic attack, an upward horn thrust. Horn thrusts can flip Koopas and jumps can flip Bug Fables enemies, so no need to subcategorize. Because player characters are allowed to conceptually vary their basic attacks, i.e. punch one time and jump the next time, they can potentially always have the option to flip a flippable enemy; if this seems problematic, you can suspend that ability, requiring them to conceptually define one basic attack and stick to it, but either way, special attacks are always specifically defined, so their ability to flip or lack thereof will always remain consistent.
An enemy that has any Defense Power will be treated as having 0 while flipped, though defensive Brain Power is unaffected. For special cases where you want the enemy to retain some points of Defense Power when flipped, you'll have to specify that in the "Notes" section at the end of the enemy sheet. With Koopas and their ilk, the shell armor is what carries the property of flippability, so a shell-less Koopa cannot be flipped; when one is flipped, the armor is essentially ignored completely, no longer protecting the wearer from any damage and no longer losing any of its own HP since it's not doing so. But it still counts as armor being worn, so it still can't be stolen until the current wearer is dead.
A character who is currently flying cannot be flipped while in midair. In contrast, a flippable character who is currently burrowing underground will, if flipped, be forced aboveground for the duration of being flipped, and if it had been granted underground...ed...ness as a Status Benefit, then this Benefit is removed completely as a result of the character being flipped. But back to flying: in Paper Mario, it was only jump-like attacks that would de-wing "Para" enemies, with other attacks dealing damage but leaving them in the air; by default in Arpeggio, any attack that deals damage (after applying defenses) will cause the wings of "Para" enemies to fall off, but if you're implementing flipping in your game, then you could make it so that only flipping attacks will remove "Para" enemies' wings. This makes such enemies a bit more strategic and flipping a bit more useful, and it could even be extended to the effects of items like the Witch's Broom, which is something that Magikoopas use to achieve the same removable flight effect.
Lastly, some Mario enemies, despite being Koopas, traditionally could not be flipped—e.g., Hammer Bros. For the sake of simplicity, since I used the same Green Shell armor for them as I did for regular Koopa Troopas, I'm saying that by default they can be flipped in Arpeggio. To overrule this, you can explain in the "Notes" section at the end of the particular enemy's sheet that it specifically doesn't get flipped even when wearing shell armor. Or you could just, y'know, make it happen that way without needing to note it.