What enemies drop Sparkle Cards?

From my experience, I have gotten 6 sparkle battle cards, 3 from shiny fire piranha plants at Twinsy Tropics, 2 from shiny paper bob-ombs at Sunbeam Plains, and 1 from a nonshiny paper bob-omb at Sunbeam Plains.

From what I have heard and read, it seems there are various enemies that drop sparkle battle cards randomly. Not only shiny enemies drop them, and not every shiny enemy you encounter will drop one but it seems you have a better chance with shiny paper enemies, because most of my shiny paper enemy encounters have given me a sparkle card, but only one nonshiny paper enemy out of a ton that I have faced, has given me one. I haven't gotten any from regular nonpaper enemies, so I'm not sure if they drop them or not.

Based off of my experience and what I know so far, I'd say your best bet of collecting them is hunting down a bunch of paper enemies and searching for the shiny ones. They are rare but at a place like Twinsy Tropics, 3 times out of 4, I have found 1 shiny out of all of the paper fire piranha plants that live there, and they haven't failed yet to drop a sparkle battle card. You are also likely to encounter some shiny paper enemies by revisiting Sunbeam plains and fighting the weak paper enemies there.

No set enemies drop them. It's just random. You can go to the Lakitu Info Centre and do some missions if you weren't aware. Make sure you're checking previous shops that were unavailable as they'll generally sell some cards.

It seems that Shiny Paper enemies drop Sparkle cards at a much higher frequency than I've gotten from other enemies. In fact, I don't recall getting a single Sparkle card from a non-shiny enemy.

Certain enemies drop certain Sparkle cards, and I've gotten plenty of Sparkle cards from non-shiny enemies. Paper Ninjis have quite a few, as do Paper Koopa Troopas. You'll know when a Paper enemy no longer have any sparkle cards to give when their rare drop gives you their common drop item instead.