Critical Mach Number has nothing (directly) to do with altitude.

Mach Number has everything to do Temperature,

Lower critical mach number may be defined as the highest subsonic mach number below which the entire flow over it is subsonic. vijayaprakaash

Critical Mach Number, or Mcr, refers to the lowest Mach number that air going over and around an aircraft can reach the speed of sound. If an airplane goes over its Mcr, handling might be greatly affected.

The critical Mach number will increase significantly

the Mach number