First is hitmonkey. By far the best mercenary champ to solo her

Took 142 and goes by fairly quick. R5 full suicides.
Next is sentinel for the villian/metal objective. If he's awakened this fight I'd imagine would go by quite smoothly, but unawakened it is a bit of a pain to get 100 charges. Either way, past a certain point he starts to get her down fairly quick to secure the objective. R5 full suicides

Lastly for the mystic objective is Magik. She may not do the most damge or take ghost down in the least amount of hits, but the way she controls the fight makes her a top option. Get ghost Power locked, trapped in the corner, and backdraft her to death. R5 full suicides.

No matter what champ you use for the objective, the fight will be fairly long. But these options make ghost just a little less painful.