I have already translated an article which spoke in depth regarding narrators of Ziarat-e-Ashura. However, I would like to present view of Syed Sadiq Rohani regarding authenticity of this Ziarat. Opinions of other scholars can be seen on this link.

He has mentioned authenticity of this Ziarat in different fatawas. Like in one fatwa, he said that

This Ziarat is reliable and there is no problem in it. [Link to his website]

And He also said

Its chains are Strong/Qawi [Link to his website]

But the one which I would like to share in totality is when He was asked regarding Sanad/chain and Matan/subject of this Ziarat, and He replied

نعم صحيحة سنداً ومتناً ، ولستُ أحتمل صدور تضعيف هذه الزيارة المعتبرة من عالم محقّق ، وإنّي ـ بحمد الله تعالى ـ ملتزم بقرائتها كلّ يوم منذ خمسين سنة ، وأسأل الله تعالى أن يديم توفيقي لذلك إلى آخر أيّام عمري .

Yes, It is Sahih/authentic as per Chain and Subject. And there is no chance of Weakness in this Reliable Ziarat in view of a Scholar who does research. And I, by the grace of Almighty Allah, have been making it sure to recite it every day for last 50 years. And I ask Almighty Allah to give me the strength to do it till last days of my life. 

[Link to this fatwa]

fatwa