The word "valiantly" is correct and usable in written English.
You can use it to describe someone who bravely faces a difficult task or challenge. Example sentence: The firefighter valiantly risked his life to save the trapped family from the burning building.
Dictionary
valiantly
adverb
In a valiant manner; showing bravery.
synonyms
Exact(60)
Importantly for Clark he now carries nothing like the weight of expectation he had at Melbourne, for whom – no matter what anyone says of his departure – he always tried valiantly.
He says: "I don't believe we could have worked any harder for a Labour victory – and we owe a great debt to the thousands of people who campaigned valiantly on doorsteps across the country.
Facing an unprecedented onslaught of piracy, his business had suffered, but he had fought valiantly to protect the industry and the artists that he loved.
While Miliband was valiantly attempting to own the future, he lost the core argument about the past.
It was a mortifying moment, made more mortifying because Robin Williams valiantly tried to salvage her mistake by leaping on stage and having the sort of multi-part conversation with himself that you'd normally expect to hear from red-eyed lunatics at bus stops at 3am.
At present, the Arts Council is valiantly trying to do some of these things, but it is far too little – and for the 75 libraries that have closed in the last 10 months, it is too late.
With Van Breuckelen and Klinsmann valiantly attempting to act as peace-makers, Loustau promptly brandished his red card in the direction of Rijkaard, before turning and showing it to Völler too.
There are those who will valiantly try to rebuild the party.
When the first officer of EgyptAir Flight 990 decided to crash his plane into the Atlantic Ocean in October 1999, killing 217, his captain fought valiantly to save those aboard, ultimately failing to over-power the co-pilot.Efforts by the industry to tighten psychological evaluations, though valid, will be equally imperfect.
And yet, polarised and unequal as Kenya is, its progress punctuated by electoral violence and spasms of ethnic tension, the country has for the most part muddled valiantly ahead.It remains the economic and political hub of wider east Africa, drawing a quarter of a billion people into its orbit.
Their soldiers fight valiantly, but with little understanding of the strategy.
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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