It's supposed to be possible if you manage to stall Foxy enough to run at you once in the whole night. I think that's the only thing that makes it as hard as it is.
I learned that, to get the plushies, you don't need to beat 4/20; you just need to beat the animatronics at their lvl 20. Which means you can take them one on one and still get the plushies. That said, beating 4/20 gives you the last 5% completion.