The rank of your crew is displayed in the garage. Press
on a tank, and then select "crew". You will see on the top right corner of your screen the rank of your crew. For example, it will say 9/17. 17 is the maximum crew rank, for all nations. By the way, the rank itself serves no purpose, it is only decorative.
Crew rank will improve with the experience earned in battle, exactly like when you learn skills and perks. You don't have anything else to do, simple play the game with the same crew over and over. Transfering a crew on a new tank will not have any impact over their rank. Therefore, using a premium tank will accelerate the process. Of course this is 100% your call: you don't have to pay to get this achievement.
According to Wargaming numbers, you need approximately 2 millions XP to get to rank 8, which means that you will have your tier X long before you reach rank 8. When you have a crew with rank 8, play with the tank until you kill 3 opponents. You can transfer the crew to another tank if you think that it will improve your chances of killing those 3 enemies in a single battle. Also, you can play on a platoon and ask your friends to let you deliver the final blow to those enemies.