From The TimeSplitters Wiki

Mr. Big
Unlocked by	Chinese on Hard in 6m
Species	Human
Size	Normal
Accuracy	N/A
Agility	N/A
Stamina	N/A
Fire Proof	N/A
Shock Proof	N/A
Default AI	N/A
Native TimeZone	1970
First Appearance	TS1 Story Mode
Relations	Big Tony (Possible Relation?)
Games	TS1

Mr. Big is the boss of many foes in TimeSplitters 1. He runs the Chinese gang and is a tall and bald man.

TS1 Gesture	Sits in chair saying "Hey, I'm a busy man!", gets up saying "Ain't got all day!", and whilst fixing cuffs says "Let's get down to business huh?"	TSFP Gesture	N/A
TS2 Gallery	N/A	TSFP Gallery	N/A

Big Tony?

Mr. Big is not Big Tony. Big Tony lived (and died) in 1932, whilst Mr. Big lives in 1970. It is possible that the two are related, since they look similar and share a similar duck-based mission in Challenge/Arcade League (See Flock Around The Dock and Someone Has Got to Pay).