My Whirlwind Barb Runs Out Of Mana In One Attack - Best Options To Solve This?

Recommendations all depend on how much you are able/willing to invest in the character.

End Game - you will want your Merc to carry Pride for the Concentration Aura. This means mana leech from rings or dual-wielding EBOTD with your Grief.

Until then, Insight runeword on a Merc is my preferred method.
Insight has a nice amount of ED, making it a good damage weapon for the merc, and provides Meditation Aura for mana regeneration.

To work best, you will want a large mana pool, regeneration speed is proportional to your max mana.
So, be sure to invest 20 points in Battle Orders and have two +3WC weapons in your weapon switch.
If your BO is high enough, then an Insight Merc even enables you to Teleport endlessly without needing mana potions (Enigma needed of course).

If you are having trouble keeping an A2 merc alive, then you can also put Insight in a bow for an A1 merc.
She is ranged, so wont take as many hits, and the Barb doesn't need an A2 meat shield anyway.
Her exploding Arrows provide nice AOE damage (which the barb generally lacks), and she fires instantly with each Teleport (very helpful if you are kiting a difficult pack).