The best way, maybe the only, to complete Nightfall with a relic is play it in co-op (4 players) with a good team, but I suggest no more than 1 player should use a relic.
There are a lot of enemies, phantoms, hunters and rhinos, so no way to use only the pistol or take more damage and do less damage, I completed it using Small wallet. (you can carry only 3000 credits and obtain less money killing aliens).
If your teammates provide you ammos and powerups, such as feral instinct or stamina, return the favor deploying armor, that's a must-have in this map (only 1000 credits but useful) and buy a good weapon, such as the Arx-160 (seems strange but I love Vector, because you have fast reloading and moving) and Sentry gun to protect the drill.
In my opinion, the perfect team is formed by 2 medics (I finished as a medic, using the relic), a weapon specialist (
his damage with weapons is fundamental against big enemies) and an engineer (drill and traps powered), using explosive ammos and sentry guns, the real key even if they are less powerful than in Point of impact.
Last tip: it's better do not use a relic if you are hunting to complete all challenges.
Hope this helps (and sorry for my enghlish, but I don't like translators)..