Hold feet to the fire

"Hold (someone's) feet to the fire "
1.To pressure (someone) to consent or undertake something.
2. To cause someone to feel pressure or stress

Basically, we can translate it into Chinese as (from basic to detailed) 「施壓」「施重壓」「施予重壓」「施予重大壓力」

To find a matching Chinese counterpart, we can use the four characters phrase 「施予重壓」/「施加重壓」(apply heavy pressure) or we can borrow an Chinese idiom that carry the similar meaning, for example:

「刀斧加身」(hold cleaver and axe on top of someone) "  threaten with death or serious harm" by extension :   " apply serious pressure " I think it is close but not matching very well. It fit " hold a gun to (someone's ) head" better.

Another choice is : 「拷逼」
Put someone's feet to fire is a form of  "torture" (拷) 
and the goal is to "pressure " (逼) someone

To make it more idiomatic we can say「予以拷逼」

I cannot think of a suitable Chinese idiom for "Hold (someone's) feet to the fire " but I think it would be nice if someone type in the English expression "Hold feet to the fire" in  CantoDic English meaning search, it would come up with 「拷逼 」/「予以拷逼」; 「施重壓」/「施予重壓」

If someone can suggest an idiom that has the same meaning,  then we can use "Hold (someone's) feet to the fire " as it's definition.