ALSO POSSIBLE: Translating a Sentence That Caught My Eye Into English (Part2 2)

The ancient citadel, with its strong ramparts and parapets, served as a final redoubt for the defenders, a bulwark against the invading forces.COMMENT: This is possible in formal English. (The sentence has an old-fashioned air, but it is possible.)

It stood as a bastion of their resistance for centuries.NOTE: If readers know who the word "their" then the original is fine. (Otherwise, specify who "their" refers to.)

I had to go cap in hand to my partner to cancel our plans.NOTE: In old-fashioned British usage "go cap in hand" is used. It is almost never used in North America. (Even in the U.K. this idiom might be dated. It seems like a relic of a bygone age.)

Be that as it may, I decided to go to town on the report to finish it tonight.” ¶
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3.He didn't see fit to explain his decision, acting with a strange kind of piety towards his own methodsALSO: The original is fine *if* you want a 19th century British flavour . . . in the 21st century, few people communicate this way.

This bold approach paid dividends quickly, helping the company scale the highest rung of the ladder in the industry, and his plan easily passed muster with the boarCOMMENT: The original is possible, although the phrase "passed muster" seems a bit old-fashioned.

I tried to catch his drift when he mentioned a potential looking glass solution, but his explanations were too mercurialCOMMENT: In 19th century formal British English, this is possible. The phrase "looking glass" is seldom used today - the term "mirror" is more common. Also, the phrase "too mercurial" is perfect for an Oxford don, but that is seldom used by most people today. Who is your target audience? When translating, it is important to think about the target audience.

The ancient citadel, with its strong ramparts and parapets, served as a final redoubt for the defenders, a bulwark against the invading forces.

All good here, just commenting that I wouldn't expect the average English speaker to actually know what "ramparts and parapets" are beyond "some part of a castle" unless they've taken interest in castles specifically before.

I had to go cap in hand to (ask) my partner to cancel our plans.

I think it sounds a little better to include the verb here, but both are fine.

This bold approach paid dividends quickly, helping the company scale thereach new heighest rung of the ladder ts within the industry, and his plan easily passed muster with the board.

"scale the highest rung of the ladder" usually refers to moving up in a formal hierarchy, e.g. political offices, promotions within a company, rankings in a sport. It's not usually applied to a company's financial performance.

I tried to catch his drift when he mentioned a potential ( looking glass (?) ) solution, but his explanations were too mercurial.

I'm not quite sure what you intended by "looking glass solution" here.

Be that as it may, I decided to go to town on the report to finish it tonight.” ¶
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3.He didn't see it fit to explain his decision, acting with a strange kind of piety towards his own methods.

or

”Be that as it may, I decided to go to town, on the report, to finish it tonight.”

Else, original sentence might be okay.

Some felt it was time that he was put out to pasture, but he clearly still had it in him to innovate, albeit inthrough unconventional ways.

Maybe put "that" in

"Some felt it was time that he was put out to pasture..."

* I added "through", since "unconventional ways" is a method.

This bold approach paid dividends quickly, helping the company scale the highest rung of the ladder in the industry, and his plan easily passed muster with the board.

I guess "passed muster with the board" is an idiomatic expression.

It felt like a Catch-22: revealing the error would get me fired, but hiding it felt wrong.

In short:
Catch-22 - impossible situation (or "Catch-22" the book?)

I tried to catch his drift when he mentioned a potential looking glass solution, but his explanations were too mercurial.

In short:
catch his drift - understand what he meant
looking glass solution - introspective solution?
mercurial - unpredictable, unstable

It had stood as a bastion of their resistance for centuries.

I'm going to be guessing a lot here, because I can't see the original text, but considering this is an ancient citadel I'd say it "had stood <...> for centuries". Otherwise you're saying it'll be a bastion for future centuries.

I had to go cap in handapologise to my partner tofor cancelling our plans.

"cap in hand" is correct, but also sounds very old fashioned.

Be that as it may, I decided to go to town on the report to finish it tonight.” ¶
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3.He didn't see fit to explain his decision, acting with a strange kind of piety towardsbelief in his own methods.

"piety towards his own methods" sounds weird. Piety refers exclusively to religious beliefs.

This bold approach paid dividends quickly, helping the company scaleclimb the highest rung of the ladder in the industry, and his plan easily passed muster with the board.