The speaker's description of the haircut as a "bright helmet" in line 15 suggests that

To get the context of the phrase "bright helmet" one would have to read the entire Poem "Possessive".

The poem artistically analyses a seemingly troubled relationship between mother and daughter. Her daughter has reached the age where there is not just an aversion for rules that adolescents can't rationalize, but also some distaste for restrictive authority.

Because the mother has to be "firm" with the rules in order to protect her daughter and the daughter wants to be "free" from "restrictions" that make her feel she is still a baby, there seems to be an ongoing "war".

The writer captures this subtle "battle for power" or "warlike situation" by using such words as:

Blade of new bangs ... (line 7) Eyes like carbon steel (lines 8-9) Bright helmet (line 15).

See lines 17-20 also.

Cheers!