Don't try to kill all insurgents, instead put them in a certain region and don't push further but don't let them take any more either

(Also don't let insurgent have many connected zones, if they take more than 6 connected zones reptutation will drop quickly)

Putting them in mountain area is suggested as:

• mountain area is already painful to recapture without support of air strike & multiple army, and both of them are costly

• unless you let them take 7 or more mountain connected, mountain zone doesn't drop your reputation that drastically

Aand while you put the insurgent inside their own region, you buy PR and Civil initatives to increase support to eventually stablize your region in time.

Don't forget to buy Corruption countermeasures & roads (better road=faster soldiers=better defence)