We've had a few questions on how the achievement works, so it seemed like a good idea to provide some clarity.
The Bloodthirsty Achievement counts the highest number of trophies that you've had at any one time. It's like a high-water mark. If your record is, say, 750 trophies, then the counter for the achievement won't move up until you have 751 or more in-hand. It doesn't count all of the trophies that you've ever won on your account.
Also, the achievement is specifically for Trophies, which are earned from world PvP (using the Battle button on the Home screen). Banners, which are earned by fighting in PvP events, do not count toward Bloodthirsty.