Colonel rank is the highest a soldier can achieve and will require them to be present in most missions. Soldiers rank up by damaging/killing/capturing aliens, performing actions like firing while on overwatch/suppressing, and surviving missions unharmed. Reaching the rank of Colonel will take time and require a single soldier to be present on most missions throughout the game. It’s a good idea to use higher ranked soldiers as the driving force when attacking, as performing more of the actions mentioned above will result in faster promotions. Also remember, when ranking up and choosing perks, choose perks that suit your play style allowing you to utlilise the soldier more effectively.
TIP: It is a good idea to work on this achievement while going for ‘Ain’t no cavalry comin’ because if you use the same soldier on every mission, they will reach colonel easily. You can also buy the 'Wet Work' perk from the Officer Training School for 125 credits that grants soldiers additional experience per kill.