Doesn't "continue to boil" work here? If not, what is the reason?
le2)How to cook Yudu Guksu: Put chicken and water into a pot. Boil it for 10 minutes on high heat. Reduce the heat and continue (to boil/boiling) for another 40-50 minutes...
It is ,however, a little strange to tell someone to bring it to the boil, then reduce the heat, but then to continue boiling it for another 40-50 minutes. Usually, the point of reducing the heat is to bring it down from a boil to a simmer. If you want it to continue boiling, you wouldn't reduce the heat.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.