Can I use the phrase 'nigh-on-impossible' in a report?

Nigh (archaic) means ‘near’.

As in ‘when winter is nigh’, nearly winter. Or ‘Evening is nigh’ - almost evening.

It still shows up in idioms like ‘nigh on impossible’ as you mention.

But that’s not what I dislike about it, for an academic report or serious piece of writing.

What I dislike about it, is that it’s rather woolly.

‘Almost impossible’

What’s that? Surely if something is ‘impossible’ it means it can’t be done. Adding ‘nigh on’ or ‘almost’ to ‘impossible’ - takes something immutable that definitely can’t be done - an imposing mountain that can never be climbed and adds a woolly little cloud to it that says ‘oooh - maybe!’

Although it is, really, correct in English it just sounds a bit - unscientific.

Instead, how about

• Extraordinarily difficult
• Highly unlikely to succeed
• Phenomenally treacherous
• Outside of predictions
• A fools errand
• A Herculean task
• Monstrously complicated
• Like an ant trying to scale Everest - highly unlikely

In other words, I would explore other more creative ways of painting a picture of the difficulty of the task without resorting to this idiom.