Where can I get small sun badge catalyst?

There is a better chance of it dropping for you on stages 4-8 or 4-9. There is no guarantee of getting it there, but according to what we have read about the game, here is a good place to try to get it.

You may have to play through the level multiple times.

You may also be really lucky and find one on 3-7 although the drop rate on that level for such a good item is pretty low. Better to try to work up to 4-7 and 4-8 and try there.

If you get it, let us know at what level and how many tries it took.

Look out for events as sometimes catalysts such as this one are available to purchase.