The best class to always get higher tiers enemies are Light Tanks.
For those who do not know how the match making works for WOT, it's usually +2 -2 tier limits on all tanks except for Light tanks.
for example a Tier V light tank can see enemies upto tier X. with this being said, choosing a tier V,VI,VII, VIII light tank will increase your chance of destroying enemies 2 tiers higher than you in one match.
Just like Rotcat's suggestion on using the Chaffee, which is also my favourite Light Tank..with a total of 2k + matches played with her, and about 1200 kills and most of those have been two tiers higher than me and even some being tier X's.
Medium tanks are great for "stealing kills" especially tanks +2 tiers higher than you due to your speed and mobility and a slightly more powerful gun in comparison to Light Tanks. Unlike Light tanks, you will have the standard match making unlike light tanks.
Heavies/TDs have better guns than the lights/mediums and if you camp, you maybe able to steal some easy +2 tier kills.
IMO the best class to get higher tier kills would be using any arty you are good at.
Artillery basically sits in the rear and picks off targets no matter what tier, higher or lower...if you pick and choose only +2 tier targets, you should be able to get this cheevo easy with any arty you choose.
Now the basic strategy: this may be frowned upon with your 14 other team mates but will certainly get you this cheevo. Steal the kills!! in a light/medium tank, zip around the map and prey on the almost dead enemies.. in a TD or heavy, you can either camp or only engage targets which are almost dead.
You need to have some basic knowledge of different tanks and the tiers. At the beginiing of the match, during loading screen of the match, hit your BACK button andhave a look at the roster.. know which tanks are +2 tiers and put the blinders on and hope you are able to get the kill shots on the higher tier tanks for the cheevo.