General Synonyms:
* Tantrum
* Temper tantrum
* Outburst
* Rage
* Fit of anger
* Meltdown
* Freak-out
* Blowup
* Ranting and raving
More Formal Synonyms:
* Emotional outburst
* Excessively emotional response
* Uncontrolled display of anger
* Irrational outburst
* Irascible reaction
More Informal Synonyms:
* Spitfire
* Screaming match
* Throwing a wobbly (UK)
* Going ballistic
* Having a conniption
* Losing it
The best synonym for "hissy fit" will depend on the specific situation and the level of formality you are aiming for.