Learn Icelandic: Stórmeistarinn er kona mikillar greindar. - The grandmaster is a woman of great intelligence.

This is the genitive of description (eiginleikaeignarfall). When you want to describe someone as having a certain quality, you put the descriptive noun and its adjective straight into the genitive case. It translates directly to the English 'of [quality]' structure, like 'a woman of great intelligence,' but Icelandic doesn't use a preposition here.

Why does the adjective take the form mikillar?

Mikillar is the feminine singular genitive form of mikill (great). It must match the gender, number, and case of the noun it modifies. Since greind (intelligence) is a feminine noun in the genitive singular (greindar), the adjective becomes mikillar.

Stórmeistari is grammatically masculine, but it refers to a kona (woman) here. Does this affect the grammar?

Grammatical gender is fixed to the word itself, regardless of who it describes. Stórmeistari is always a masculine noun, so it takes the masculine definite article (-nn). It is perfectly normal in Icelandic to use a masculine noun for a person's title and link it directly to a feminine noun like kona using the verb vera (to be).

Is greindar related to the adjective greindur (intelligent)? Could I just use that instead?