From The TimeSplitters Wiki

Time Assassin
Unlocked by	Beat "The Hooded Man" on Normal
Species	Human
Size	Normal
Accuracy	N/A
Agility	5
Stamina	5
Fire Proof	5
Shock Proof	5
Default AI	4
Native TimeZone	1924
First Appearance	TSFP Story Mode
Relations	N/A
Games	TSFP

TS1 Gesture	N/A	TSFP Gesture	Slashes sword across screen and says "I'll slice you up!"
TS2 Gallery	N/A	TSFP Gallery	Highly trained ruthless killers with a reckless disregard for the consequences of their temporal shenanigans. These guys would quite literally kill their own father, or grandfather...or any other ancestor really, they're not too fussy.

The Time Assassins were sent from 1924 to the year 2401 in order to assassinate Cortez. Their plan failed because Cortez received cover fire from his future self, who was disguised as Time Assassin Cortez.