Griever

'An important trademark' - Griever is Squall's animal trademark (and one of Square's).
'A gift to a girl' - relates to Squall giving Rinoa his Griever ring (even though the pass 'relay' was from Squall to Zell to Rinoa) as a gift.
'Ultimate power' - refers to Squall considering Griever to be a GF of 'ultimate power'.
'Drawn from one's mind' - Ultimecia draws Griever from Squall's mind.