According to
Knaurs Vornamen Buch, published in Germany in 1985, Hilma, like
Helma, is simply a pet form of Wilhelma or
Wilhelmina, the
German feminine forms of
Wilhelm, which is itself the
German form of
William. My Dutch name dictionary gives the same explanation.
However, my Norwegian name dictionary,
Norsk Personnamnleksikon by
Ola Stemshaug, explains Hilma as a feminine version of Hilmar, which is itself a shortened version of Hildemar, which is from old Germanic words that meant "battle" and "famous."
My interpretation would be that Hilma, like many short forms, has two different legitimate variations from two different Old Germanic names,
Wilhelm and Hildemar.