Kestrel Falco tinnunculus, Faucon crécerelle.
TN 2 5 115 p And with what wing the staniel checks at it!
Staniel, Stallion, etc are all corrupt and dialectal forms of the name of the Kestrel. It is the smallest raptor of the British Isles. It was considered useless for the purpose of falconry - except probably for training - as is made clear by the quotation from the Boke of St Albans that Barry HINES chose to use as a title for his novel A Kestrel for a Knave, later made into a film, Kes, directed by Ken LOACH (1970).
In Twelfth Night, when Malvolio catches sight of Maria's concocted letter lying on the ground, Fabian exclaimed: "Now is the woodcock near the gin." (2 5 84), meaning that the prey was close to the trap (see WOODCOCK), a moment later he adds "What dish o' poison has she dressed him!". To which, Sir Toby replies: "And with what wing the staniel checks at it!" (TN 2 5 115 p).
This is another metaphor drawn from falconry, but the raptor used here is the basest. In addition, the verb "to check" bears a special meaning, it is used to describe the way the falcon sometimes "forsakes her proper game and pursues some baser game that crosses her flight" (OED).
Both woodcock and kestrel are used to describe Malvolio as he is about to be fooled, but they refer to a different social background, the aristocratic art of falconry, or the practical activity of fowling, thus appealing to the different social layers of Shakespeare's audience.