If you don't want to buy a [Banshee Prime] set while she's off the Resurgence rotation. This is an adequate starter build for star chart and lich hunts, with great energy economy and decent durability. Adapts easily to her Prime by fitting [Equilibrium] to the additional Dash polarity.

Upgrade path:

Swap [Vitality] for [Adaptation] and Arcane Blessing. Molt Augmented will increase the multiplier on your Sonar.

Also see my "No Brain [Banshee]" for an infinite scaling build.

In depth:

[Banshee] is notorious for two things: being paper thin, and dealing a lot of damage to Demolysts and liches.

The addition of Fractured Blast and Lycath's Hunt gives us a way to turn any frame into a tank that can scale comfortably to level 200 or so, well beyond what is needed for liches. These abilities rapidly spawn health orbs, allowing Arcane Blessing to stack within minutes, and maintain full stacks on [Health Conversion], for a large amount of healing and EHP.

In particular, we want to apply this idea to [Banshee] as she has an amazing kit for lich and sister hunting: [Sonic Fracture] eliminates sister armour, Silence locks out their annoying ability casts, and Sonar places an extreme damage vulnerability effect that bypasses the lich DPS cap.