UPDATE: There have been multiple reports of this achievement not working/tracking correctly lately--please read some of the later comments for some different ideas of what is happening. Keep an eye on your achievement progress tracker, and see if it is tracking properly!
This is either as easy or as hard as it sounds depending on how much you like low Tier tanks. They can be any enemies, from a mix of countries, you just have to get any 5 kills each with any 5 different Japanese tanks for a total of 25 kills. (You can sell the tanks after you get the 5 kills, not keeping all 5 at once--thanks for the reminder VegaDark541 and xxvadi!)
I personally did this with the first 5 available Japanese Tanks:
Tier 1: R. Otsu
Tier 2: Ha-Go and Chi-Ni
Tier 3: Ke-Ni and Chi-Ha
It's simply a matter of playing. I highly recommend getting the upgrades for the tanks though, and if you like close quarters fighting, the multiple shot upgrades are a must.