What is Elite quality?

You can't see that a fresh catch is Elite. Its grade reads "Unappraised" until you submit it in a catch report at an Outpost's Research Console, and only then do you learn whether you have an Elite or something lower.

Elite matters because the grade sets the stat ceiling. An Elite Aniimo has higher stats than a Common or Good one of the same level and personality, and lower stats than a Perfect one. The bar for Perfect is specific: both inherent potential values have to be 8. An Elite falls short of that, and because innate potential is randomized for each Aniimo, two Elites of the same species won't have identical numbers.

Once your catches are appraised, the storage box can filter by Potential grade. Setting it to Elite lists every one you own. Rarity is a separate filter that covers Alpha and Prismana, and a Prismana form isn't guaranteed to be Perfect. A sparkling Elite is therefore a real result, not a contradiction.

Where Elite Aniimo come from

Incredible Eggs, also called Elite Eggs, are the reliable source. You find them in places such as Beast Fang Ridge, and they guarantee a hatched Aniimo with Elite potential or higher. The Ultra Aniipod also carries a guaranteed minimum, but what it guarantees isn't settled: it is given as at least Elite potential and also as at least Epic quality.

Using a Sparkling Cube on an egg or a hatched Aniimo with guaranteed Elite potential is described as raising it to Perfect. That isn't confirmed, and the Cube may still roll imperfect stats. It never lowers quality, so the worst case is the Elite you already had.

Elite to Perfect

Training in the Awaken Potential tab uses Stardust, Star Sand and Star Essence, and it builds acquired potential. That isn't the innate grade the console appraises. One description of innate potential says it can only be raised with special items such as fruits. Until that is settled, you should expect an Elite catch to stay Elite.

Not settled: The tier names aren't fixed. Elite usually appears in a four-tier scale of Common, Good, Elite and Perfect, but some three-tier versions (Common, Rare, Perfect or Good, Excellent, Perfect) have no Elite at all. Whether an Elite's innate grade can be raised to Perfect is also not settled.