*ONLY WORKS WITH THE PSN VERSION*This trophy is indeed possible, but you need to purchase the PSN version from the Store in order to unlock it, in the retail version is unobtainable.
The unlock requirements are completely different than what the description says, infact, you will need to "win 50 times in a row". Fear not, this is infact easily boostable with a friend.
First of all, log in Theater of War with your boosting partner and choose a mission where both of you are enemy. The missions change every day (after ceasefire), so try to play one you and your partner can find each other.
Once you are both matched together, who is going to lose deploys in the briefing screen (where you can select your units) all choppers and APCs (light transports) for a faster evacuation. The winning player can just skip this part by pressing Start once in the screen.
When the game loads, the losing player hold the O button and choose "Evacuate" (or simply orders all units with the mic to do so). All units will flee the gamefield and a countdown will display, just let it expire and the match will be over. Now just rinse and repeat other 49 times
It may take from 2 to 3 hours, depending of course if the servers don't log you off, randoms joining or any other problem. In case the winning player gets a random during matchmaking, he must immediately open the XMB by pushing the PS button, go to "Account", press Triangle then select "Log off". Then he can log on again, this won't break the winning streak.
If you encounter the same random in one mission, just play other missions, the winning streak can be done even in multiple missions. You can check how many winning you have by highlighting the mission and reading the text box in the bottom-left part of the screen.
The trophy may not unlock after exactly 50 wins, so keep trying (my friend nico0777 had to win 55).
Remember that if you are going for the platinum, you need both retail and PSN version because some trophies won't unlock in PSN and Dog of War is the only glitched in the retail.