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The phrase "achieved through this" is correct and usable in written English.
It can be used to indicate that a certain result or outcome has been accomplished by means of a specific method or process.
Example: "The desired results were achieved through this innovative approach to problem-solving."
Alternatives: "attained via this" or "realized through this".
Exact(38)
"The example here demonstrates to communities hurting all over the country that positive results can be achieved through this type of cooperation".
So it follows, the plays are telling us, that Queen Elizabeth I, a granddaughter of this first Tudor, will continue to reign in peace, in the golden age that was only achieved through this turmoil, sacrifice and bloodshed.
"This gesture advanced the global message on the importance of children's issues in a unique way, and we are incredibly proud of what has been achieved through this partnership".
The employee continued, "What is wonderful about now is this bit of it is being opened, and I think it is bloody important, because something as catastrophic as Brexit and Trump — the technical possibility of that — is achieved through this dark shit.
The results show that a better organization of resources is achieved through this scheme.
However, in the current market, there are significant limits to what can be achieved through this measure.
Similar(22)
This is achieved through the insertion of what Franco Moretti, the literary theorist, calls "fillers".
Most of this is achieved through the slightest of facial tremors in unforgiving close-ups.
This is achieved through the Expand_Vertex and Select_Vertex functions.
What do you hope to achieve through this resolution?
"There's a number of things we wanted to achieve through this launch — one of those, primarily, was to give people a taste of the text prediction technology".
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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