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There is a YouTube video with the following title

WestWorld Delores Goes Ozymandias On Man in Black Season Finale 1x10

Who doesn't know the tv show and this particular scene, here is a little background: throughout entire season Dolores was afraid and submissive toward Man in Black, but in the end she fights back saying the following:

I'm not crying for myself. I'm cryin' for you. They say that great beasts once roamed this world. Big as mountains. Yet all that's left of them is bone and amber. Time undoes even the mightiest creatures. Just look what it's done to you. One day, you will perish. You will like with the rest of your kind in the dirt. Your dreams forgotten, your horrors faced, your muscles will turn to sand, and upon that sand a new God will walk, one that will never die, because this world doesn't belong to you or the people who came before. It belongs to someone who is yet to come.

Ozymandias it's the title of a poem by P. B. Shelley and here are the lines which bear some resemblance with Dolores's words:

My name is Ozymandias, King of Kings; Look on my Works, ye Mighty, and despair! Nothing beside remains. Round the decay
Of that colossal Wreck, boundless and bare
The lone and level sands stretch far away.

Is it possible that the author of the video mistakenly used "Ozymandias" in the title? Or is there a meaning in "going Ozymandias" expression?

Yes, the context is somewhat confusing. "Ozymandias" is both the title of the poem and the name of the subject of the poem. In this case, I think the video creator means that Dolores talks in a style that is reminiscent of the poem (not the subject of the poem).

The poem is about how death conquers all and even the mighty are eventually all but forgotten. Ozymandias the person may have been King of Kings once, but now he is forgotten, and even his statue is buried. The man in black is powerful now, but Dolores reminds him that he will be forgotten in time, so he’s just like everyone else. Her speech carries the same message as Ozymandias the poem.

There is another possibility. Ozymandias is a character in Watchmen. Without giving too much away, his character arc surprises some of the other characters, but I cannot see marked similarities between him and Delores, so I suspect it’s referencing the poem.

'Going Ozymandias' is nothing but 'behaving or acting like Ozymandias'. It is just like saying 'going Shakespearean' when someone begins to speak poetically or uses idiomatic expressions.
In the context you gave, Delores is basically challenging her opponents, speaking highly of herself and talking about the end and defeat of anything seemingly mighty before her, just like Ozymandias did.