Greater Anchors are Blight Anchors with a large amount of health and the ability to summon guards of the Withered Aegis. These sometimes spawn in certain locations but usually Lesser Anchors spawn.
The Anchor has a wide range AE, doing damage regularly. Stay out of that are and pull the existing waves of enemies to there. Kill them down to a minimum, then head directly onto the Anchor.
Once another wave pops up, kill the mobs and return back to the Anchor. Burning Archer, a Multicasted Volcano or similar area damage spells are known to work very well on the waves.
Resists: It appears the Greater Anchor buffs itself with a heavy armor / resist buff. This should be dispelled accordingly to make any damage at all. Ice and Flame has been known to work well then.