Concentrate on the following part:
"animal-hide shields with wooden
frames were essential items of military equipment,
//a method to protect// warriors against enemy arrows
and spears"

Narrow down it further:
"animal-hide shields (with wooden frames) were essential items (of military equipment),
//a method to protect// warriors against enemy arrows
and spears"

Removing the bracketed parts:
"animal-hide shields were essential items,
//a method to protect// warriors against enemy arrows
and spears"

Explanation:
"animal-hide shields were essential items" gives us some information about the animal-hide shields and not hinting us a method. Had it been "using animal-hide shields ...", it would have hinted a method. so "a method to protect" is not correct.
option(B)- "as a method" is also wrong for the reasons mentioned for option (A)
option(D)- "as a protection of " is wrong as it won't suite for a continuation after a "comma" (after "military equipment")
option(E)- "to protect" is also wrong for the reasons mentioned for option (D)