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The phrase "be unachievable" is correct and usable in written English.
It can be used to describe a goal or objective that cannot be attained or accomplished.
Example: "Setting such high standards can sometimes lead to projects that may ultimately be unachievable."
Alternatives: "be unattainable" or "be impossible to achieve".
Dictionary
be unachievable
adjective
That cannot be achieved (or only with great difficulty)
synonyms
Exact(46)
Do we believe these things to be unachievable, unknowable or worthless?
This may be unachievable and it is possible that the Tories may end up arguing to leave.
He always had that in his mind as the goal of his life, but it proved to be unachievable.
It has taught my children to give back to community and to never give up trying to achieve what appears to be unachievable.
Its reinclusion into the global trading system, while remaining conditional on progress, must not be made so distant as to be unachievable.
A goal of €2.6bn had been set for 2013 but the lack of bids for Depa signals that even that modest target might be unachievable.
Similar(14)
Perhaps none of these aims are unachievable.
It was a lovely goal, but it was unachievable.
It goes without saying that this is unachievable... or is it?
That is partly the consequence of setting a target for net migration that was unachievable.
"Hadi's government is morally bankrupt and their dreams of coming back to Sana'a are unachievable.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com