From The TimeSplitters Wiki

Bags of Fun is part of Elite League in Timesplitters 2. It is said to be THE toughest mission in the game to get a gold, and is up there with Atom Smasher on Hard mode if you're going for the gold.

Bronze: Nothing Silver: Big Hands Cheat Gold: Ringmistress, Roman Hat for Silly Hats

Walkthrough

  This is the toughest arcade match in Timesplitters 2.  However, once you get a hang of it, you'll 

see it's a tad bit easier than it seems. First off, I'll give you the introduction.

  This is a Capture The Bag at the Ice Station level, where you're bag is at the top of the middle building, and the 

enemy bag is on that little metal ground jetting out from the edge of the level. You are Corporal Hart

and you're only teammate is Seargent Cortez, who is surpirsingly helpfull at times.  You are fighting 

about six computer characters, which consist of Reaper Splitter, Drone Splitter, and Scourge Splitter. You all start with the Plasma Autorifle, and the only other weapons are the Rocket Launcher and Homing Launcher

(which nobody will use).  

  Now, when you start, head down the stairs and straight from the strairs through the left doorway. 
There will be a speed pick up nearby, and once you get it, head right and go around to see their base. 
Hopefully there will still be a bit of armor on the hill right to the side of their base.  

Grab it and get their bag; don't bother shooting them unless they are on the small bridge right before their

base, and if they are, use the plasma grenades.  Once you have their bag, head forward to your base 

while STRAFING (the most important part.) Once you score, if you need health, look straight ahead and on the floor right below is a health powerup for full health. Get on the landing across from you (so you're above the health) and drop down o get it. If you miss, just get the half-health powerup on the bottom floor and then head back to their base. If you get it, go through the window right in front that should be straight to their base. If you don't need health, then go through the right window and get the midget powerup nearby, then head left to go to their base. Now just get the bag and once you score again, the speed powerup should be back so if you don't need health, just keep gong back and forth between the speed and midget powerups (and don't forget the armor on the hill right before their base!)

  If they ever get your bag, don't wait at you base for Cortez to get it.  If you're at your base when they 

get it, kill them. If your heading for or at their base, grab their bag and head back to your base you should run into the one with your bag, so launch a sticky grenade on him and pick it up. If they do make

it back to their base, as long as you have their bag, they'll just stand there, so just launch a grenade 

while strafing. Keep in mind that right in from of their base is the cloak powerup, which they will normally

get.  So keep an eye out, as there bag guy may b invisable.  Grab the cloak powerup when you can to prevent
them from using it.  

  I found the Plasma Autorifle to be most effective, but if you want, you can try the missile launcher if you're
having trouble.  Don't bother with the homing laucher, as it takes too long to get (it's in the buildings in the
corners.)  If you are not going for the gold, then once you have enough, get to your bag and go on the platform 

across from it with a rocket launcher (so that you can see when they come up the ramp) and shoot them. If you

are going for the gold, just keep repeating this stragedy.  Keep in mind you need 7 MORE, 5 MORE, or 3 MORE 

bags than the other team and not just 7, 5, or 3. So for example if they get two, you need five to get a bronze.

Good luck and I hope this helps!