The hellcat's 76 mm gun has strangely, very poor damage and penetration, acting almost like a BB gun, it's speed is achieved via sacrificing armor. There's is only one inch of aluminum between the crew and a incoming round. Hellcats are usually destroyed by 2 shots, if it's facing a Tiger or a Pershing, the Hellcat might not even survive the first round.
Stay in hidden and far away spots to avoid fire, shoot 3-4 rounds and then retreat again. Upgrading the engine, then gun and armor to max out it's destructive potential. It's very popular amongst top players, they use the Hellcats speed to stay of of incoming fires way and it's rapid fire capability can cause lots of critical hits to disable engines and turrets.
Capture the flag and King of the hill is the best modes for Hellcats, thanks to it's great speed, allowing them to rush to the capture zone quickly.