Common Rarity:

These chis will include color and most likely an accessory or two. Endearing, but again, they're fairly common.

Rare Rarity:

These chis will most definitely include color and an accessory or two! They'll also most likely have lineart changes, and may have a rare mutation.

Special Rarity:

These chis will include colors, accessories, and just about anything I can possibly add. Guaranteed lineart changes, and may have two or more rare mutations and/or a special mutation.

Rare:

Extra Fluff - These chihuahuas have extra fur! How soft!
Spiked Lashes - ... What? Is this the chihuahua trying to slay?
Heterochromia - These chis have different colored eyes, most often on opposite sides of the spectrum from one another. How interesting!
Wings - These gremlins have wings-- whether that's a good or a bad thing is left to your interpretation.
Poodle Fur - These chihuahuas have cloudlike fur on their necks, ankles, ears, and a small poof for a tail! How cute!
Aquatic - Wow! These chihuahuas are semiaquatic and built for living in rivers and tropical areas, but have decided to come and live with you instead!
Tailless - These chihuahuas have no tails. That's all there is to it.
Ear Mouths - These chis have mouths built into their ears! Cool-- but that leaves pats on the head completely out of the question. You wouldn't want to lose a finger if it was in a bad mood! [ Credit: Cicada (#319769) ]

Special:

Melted - These chihuahuas' crates were too hot, and they have become liquid. Oh well. They're still just as loud as normal chis, though.

Biblical - These chihuahuas aren't much of chihuahuas at all-- they have ascended past that name. As banishers of all evil and holders of power that mere mortals such as ourselves could hardly dream of, it seems kind of hard to imagine how these ended up in the gacha.