From The TimeSplitters Wiki

Can't Handle This is a honorary Arcade League challenge. It is one that commonly gets players stuck in the game, and is indeed one of the hardest arcade challenges. It takes place in Hatchet Sal's nightmare.

Attributes

• Game: TimeSplitters 2
• Mode: Team Deathmatch
• Briefing: Welcome to Hatchet Sal's cheese induced nightmare. Well, at least now we know what Big Tony's left hand man looks like. Just goes to show, if you mutilate people for a living you've got to expect to lose some sleep.
• Map: Nightclub
• Goal: 40 kills
• One shot kill: No
• Weapon(s): Retro Set
• Character: Hatchet Sal
• Win Requirements:
  • Bronze: 40 kills in 4:00 minutes
  • Silver: 40 kills in 3:30 minutes
  • Gold: 40 kills in 3:00 minutes
  • Platinum: 40 kills in 2:40 minutes
• Rewards
  • Chasm - Bronze
  • Hatchet Sal - Silver
  • Handyman - Gold

Stragedy

There is one known way of how to actually beat this challenge. Go to the story-mode entrance (down the stairs of the big lobby) and at the end of the corridor there is a Tommy Gun (x2). Go a bit forward and into the glassed area to the right of the exit to the lobby. There should be a Health Pack in there. Stand behind the pack and wait for the Handymen to come around the corner. As soon as you see one, shoot it (preferably at the head) until it dies. Continue until you die, in which case go back to where you were, and repeat stragedy. If you run low on health, just get the pack right in front of you.

Trivia

• In the pause menu, on the score section, instead of saying "kills" the section says "hands".
• The game doesn't count the enemy's kills, but instead just cares about you getting 40 kills.