In a mission profile, there are various phases such as Climb, Cruise, and Descent (excluding other phases). My question is during which of these phases, the Mach number of the airplane is highest? Is that Mach number more or less than critical Mach Number?
Mach number is likely to be highest when the aircraft is highest.
Mach number is related to true air speed (TAS) while the power required is related to the indicated air speed (IAS). As a plane flies higher, the air becomes thinner. Typically a plane will fly at a constant IAS, so the aerodynamic forces remain constant, but the TAS (and ground speed, and Mach number) increase.
As a plane burns fuel and gets lighter, it can fly higher, so just before the descent could be the highest Mach number.