You need the Covenant or Artorias (The ring) in order to traverse the Abyss and fight the four kings.
But you Don't need the ring in order to traverse the very same Abyss and fight Manus.
All lore-sources say that the abyss that Manus is spreading, and the Abyss the four kings are in, is the very same Abyss.
Actually, Artorias has according to lore-sources throughout the game traversed the Abyss with his ring when New Londo fell, and Then traveled to Oolacile to fight Manus in his Abyss.
Are these the same Abysses? Or is the Four Kings-Abyss the 'real' Abyss, while the Manus-Abyss is just called the Abyss because it's very dark, very big, and very corruptive?