I remember some rules existing about certain skills being inappropriate for animals, or beyond their ability to use — either they don't get to take them in the first place, or the GM can forbid them (for some reason other than rule zero).
I'm looking for these rules so I can add support to another answer of mine. I know it's in the books somewhere, but I can't find it.
If the DM wants no dancing cats in his campaign, the DM can rule that cats can't put skill ranks into the skill Perform (dance) and cruelly further rule that cats always fail Perform (dance) skill checks. Such a campaign is a much sadder place for such a house rule, but there it is.
For reasons I don't pretend to understand, an animal companion with an Intelligence score of less than 3 is restricted in the skills into which it can put ranks:
Animal companions can assign skill ranks to any skill listed under Animal Skills. If an animal companion increases its Intelligence to 10 or higher, it gains bonus skill ranks as normal. Animal companions with an Intelligence of 3 or higher can purchase ranks in any skill. An animal companion cannot have more ranks in a skill than it has Hit Dice.
Animal companions can have ranks in any of the following [animal] skills: Acrobatics* (Dex), Climb* (Str), Escape Artist (Dex), Fly* (Dex), Intimidate (Cha), Perception* (Wis), Stealth* (Dex), Survival (Wis), and Swim* (Str).
All of the skills marked with an (*) are class skills for animal companions.
Emphasis mine. Thus, for example, with its Intelligence score of 2, the typical small cat animal companion can't put ranks in the skill Perform (dance).
However, typical creatures with the type animal have as class skills Acrobatics, Climb, Fly, Perception, Stealth, and Swim, and the section on Monster Creation under Skills and Feats says that after deciding to create an animal the DM should
determine how many skill ranks your creature has based on its type and Hit Dice. Assign these ranks as determined by the creature's concept. A creature's class skill is determined by its type. Creatures with a low Intelligence typically only have ranks in Dexterity- and Strength-based skills.
Thus, while animal companions are limited in the skills into which they can have ranks, animals that aren't also animal companion aren't limited in the skills into which they can put ranks. This means that, for example, the typical stray cat could put its single skill rank in the skill Perform (dance) were it so inclined.1
Note that, because the skill Perform (dance) is a never a class skill for the typical cat—be it an animal companion or not an animal companion—, only a rare cat will be a truly great dancer.2
1 Dignity, however, likely means it won't.
2 Animal companions are also strictly limited in their selection of feats, requiring an Intelligence score of at least 3 to pick from any feat rather than a limited list, but typical creatures of the animal type have no such restrictions. For example, a cat could take—but an animal companion small cat couldn't—the feat Prodigy, yet either could take the feat Skill Focus (Perform [dance]). (It's unfortunate that neither the typical Charisma 7 cat nor the Charisma 6 small cat animal companion with Intelligence 3 meets the prerequisite for the feat Noble Scion of the Arts.)
You can train a cat to dance using Handle Animal - but it's quite hard to do so!
Entertain (DC 25): The animal can dance, sing, or perform some other impressive and enjoyable trick to entertain those around it. At the command of its owner, the animal can make a Perform check (or a Charisma check if it has no ranks in Perform) to show off its talent. Willing onlookers or those who fail an opposed Sense Motive check take a –2 penalty on Perception checks to notice anything but the animal entertaining them. Tricksters and con artists often teach their animals to perform this trick while they pickpocket
Thus it doesn't seem to be a thing that normal-intelligence-cats put ranks into... However if you do teach them Entertain first, maybe they should be able to take ranks in Perform after?
If not give them an intelligence boosting headband with the perform skill built-in... - If that's to big of a financial investment, then you're probably not level 20 yet...
Maybe you can work something out with your GM (i.e. use his Rule Zero to make something awesome otherwise not in the rules happen with that cat) -- otherwise your cat is out of luck.
Another thought: Dancing isn't a skill that requires you to have ranks in it to do it - only to do it well. Thus your cat could theoretically dance on it's own will, though with an intelligence of 2 it probably wouldn't even know what the heck dance means...
According to Animal Companions rules, animals can only use Acrobatics, Climb, Escape Artist, Intimidate, Perception, Stealth, Survival, and Swim. Unless a druid raises his animal companion's Intelligence to at least 3 ; then it can learn anything (but not always use everything : a cat cannot craft a weapon , a dog cannot climb ladders or trees).
Some feats exist for non-druids to have an animal companion :
You can also try to use an Intelligence-boosting magic item, but it needs to be worn for 24 hours straight before the new ability score can be considered permanent, and any removal or dispel will disable everything it required.
I hope I helped. Personally, I'm not too fond of house ruling, I prefer looking for nice stuff in rulebooks.
