Yeah, sorry, I was already at over 1600 badges when the statue update rolled out, so I had already exceeded the necessary amount for level 10. Since the bunny didn't always say what the requirements were or the number needed show up on the statue (for example, the number on the statue stayed at 999 for several resets of my game as I was leveling), I don't know the list. You do need 1000 or some number above that for the max though.
The number is unique badges, duplicates don't count. Large badges (ones that span 2+ spaces) count as however many spaces it takes up.
But once you get close to hitting 1000 unique badges, you have other things to worry about (using the Badge Box and saving home layouts).
Edit: might as well explain the Badge Box since people can use them already...
VERY IMPORTANT INFO ABOUT THE BADGE BOX
What is the Badge Box?
The system has a limit of 1000 unique badges that you can have out at any given time for decoration (for hardware reasons). The Badge Box is a fridge you can use to retire badges you collected.
Where do I access the Badge Box?
Talk to the bunny at the information booth.
How do I use the Badge Box?
The bunny explains this. You retire categories at a time -- e.g. Super Mario Bros., Animal Crossing Items, Splatoon, Pixel Collection, etc. You can always shuffle them back out, but you always have to have less than 1000 in total.
The bunny gives a fair warning every time, that any time you commit a change of the contents of the Badge Box, all of the existing badges you have out on your home screen will be put back. Rather than manually placing them again, you should save your home layout so that you can easily restore everything after you make changes to the Badge Box.