Kill Godfrey (Gold Spirit)
To complete this square you need to defeat Godfrey, First Elden Lord (Gold Spirit), the boss in Leyndell, Royal Capital. Wait until the "ENEMY DEFEATED" or equivalent screen appears to mark the square.
To reach Godfrey you need Capital access, which entails defeating two Great Rune bosses. This square has synergy with Kill 4 Bosses with the word God in it and Kill 5 Bosses in Altus Plateau/Mt. Gelmir.
Godfrey counts as an Altus Plateau/Mt. Gelmir boss.