To "levy criticism" or to "level criticism?"
It's just "levelled" or "level"
"level" simply means "aim" (as in, aim a gun). It's verb definition 4 in the OED
4 [ with obj. ] aim (a weapon): he levelled a pistol at us. • direct (a criticism or accusation): accusations of corruption had been levelled against him.
This really ignorant mistake in the "New York Times" (which used to be a "newspaper of record") helps us remember an important fact about language in the English-speaking world of today:
Standards are incredibly low.
It's common to find on this site, questions about something which is actually just a complete editing screw-up by a major publication -- such as the example here.
Ignorant though it might be, the use of "levy" to mean "level" has a long pedigree. The above-cited OED has this as meaning no. 7:
- Wrongly used for level v.1
1618 N. Breton Court & Country (Grosart) 6/1 Winking with one eye, as though hee were leuying at a Woodcocke.
a1635 T. Randolph De Histrice in Two Poems (1638) 26 Fam'd Stymphall, I have heard, thy birds in flight Shoot showers of arrowes forth all levied right.