Woot, just completed the SC2 mastery achievement Anvil of Will! It is probably one of the hardest mastery achievements in LOTV. I think one of the major factors that helped me in winning (besides doing some research beforehand) was Solar Lancing the baneling waves that come out at the 1.45 billion zerg mark at around 29m30s game time. Also, whenever structures were destroyed, I spam built pylons in their place to keep future waves from reaching inwards to do more damage.
My Spear of Adun abilities were:
a) Chrono Surge - use on building probes to max out economy early on
b) Solar Lance - kept on cooldown to clear as many baneling waves as possible
c) Nexus Overcharge - build 3 Nexus at each entrance supported by shield batteries
Key ideas to beat this achievement:
a) Take 2nd base asap
b) Chrono surge to boost economy
c) 3 Nexus at each entrance supported with shield batteries
d) Build Khaydarian Monoliths/Shield Batteries all over your base
e) No need to destroy Zenith stones for this achievement (note that this will result in a failed mission)
f) Stay alert for baneling waves at around 29m 30s mark, around 1.45 billion zerg. Keep Solar Lance on cooldown to clear as many baneling waves as possible. In between baneling waves, build pylons to delay incoming enemy waves from pushing inwards.
I spent about 1 hour getting this achievement, including reloading time for saved games.
Good luck with this achievement!