From The TimeSplitters Wiki

Escape from NeoTokyo
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Game	TS2
Section	Infiltration
Map	NeoTokyo - Streets
Character	Chastity
Enemies Encountered	N/A
Rewards	?: Big Ears hat
Medal Requirements	Bronze: ? Silver: ? Gold: 1000 points Platinum: 1000 in ? secs

Escape from NeoTokyo is one of easiest challenges, because all you have to do is get to same place you have to go in end of NeoTokyo story level, but unseen by Spotlight Cameras.

Briefing

Strategy

Well this actually don't need any strategy told, just do all same like you do NeoTokyo on normal difficulty, when you have to go that way after killing Sadako. If you get busted, you lose. Just dodge the Spotlight Cameras until you reach end of NeoTokyo level.

If you're not so crazy about getting golds and platinums. Just run down the centre of the street, you'll get a bronze or a silver. Fail, you're doing it wrong.