Flight Delay is Challenge 9-B in the original TimeSplitters. It involves escorting a Spaceways Stewardess through the TimeSplitter-infested Spaceways space port and into the rocket. It comes after I Can't Hear Anyone Screaming and before Space Vandals.
The TimeSplitters flight is delayed and they're getting bored and restless in the departure lounge. Consequently, the Spaceways Stewardess needs an armed escort to the departure gate.
This isn't a particularly difficult challenge. Although this is one of the longer Escorts, the Splitters like to waste time doing their little taunt before actually attacking. And even then, their attacks do very little damage to the Stewardess. Just get a Scifi Autorifle and gun them down. If you can find a Rocket Launcher, it is also effective. Don't worry about shooting the Stewardess yourself, Friendly Fire is disabled for this challenge. Just keep an eye on your radar and shoot the splitters when they turn up.