Warning: Nelgirion the Venerable is one of the strongest enemies in the game. Come prepared.
His only real weaknesses are physical damage and absorb health (because absorb health won't harm you if reflected). Your best options for defeating him are to drink a bunch of sujamma and try to kill him as quickly as possible. Or use absorb health combined with weakness to magicka.
Alternately, you can quite easily push him into the large pit that appears on your left as you approach his chamber. Any creature, Nelgirion included, will take constant damage while at the bottom. Between his large pool of health and his restoration magic, it'll take a while, but he will eventually die with a minimum of fuss.
The following Journal ID and Index codes can be used with the Journalconsole command to manually update the quest to a certain point.
Anti-Magic (TR_m7_Ns_MG_Arch03)
Index
Finishes Quest
Journal Entry
10
Mhas Vathor told me that using the Amulet of Passwall inside of Alta Vathor would bring me to Archmage Ysadora outside of space.
20
The Amulet of Passwall shattered after I used it to travel outside of space.
50
Ysadora Bellette was freed from her prison after I defeated the lich Nelgirion the Venerable.
70
Mhas Vathor sent Ysadora Bellette and I back to Narsis.
75
%Name, of the Narsis Mages Guild, told me that I should seek out Ralsa Ondusi, as she wants to speak with me.
100
Finishes quest
I spoke to Archmage Ysadora in her chambers in the Narsis Mages Guild, confirming that she was returned safely.
105
Finishes quest
I brought the amulet of Passwall to Archmage Ysadora. The spell was lost forever, but Ysadora was able to recover a fragment of Nelgirion's anti-magic curse, which she taught me how to cast.
110
Finishes quest
I brought the amulet of Passwall to Archmage Ysadora. She used it to teach me the spell.