Unreal Tournament 3

DarkSynopsis has a good method, but here is another solid method that worked for me.

Start a Duel game against a Godlike bot, on the level Heat Ray. Enable the Weapon Replacement mutator, set for Impact Hammer.

Hide or run from the bot for a few minutes, after a short while, a Darkwalker will be dropped onto the platform. Just make sure you get there first, get into the Darkwalker, and the rest is easy! Blast the 'bot with the Darkwalker whenever you see it.

Good Luck!

Here is a rather easy way to grab the Untouchable Achievement

From the menu go Instant Action then Duel and pick Deimos map, Now make sure the Bot Skill Level is on Godlike then set Goal Score to 20 and Time Limit to 60.

Once that is set hit X for Mutators and add in Low Gravity and Weapon Replacement and set all weapons to Impact Hammer

Now enter the game and head for the Orange Portal will takes you up to the turret and now you just got to sit there and take out the bot when you see it.

Video: http://www.gamevee.com/viewVideo/Unreal_Tournament_3/XBox_36...

Here's a video I made showing d3vilsNight's solution
(I personally prefer visual aid)
If this video helped you please vote up so others can see it
and if it didn't and you vote down please say why so I can fix it
Thanks and Have a nice day :)

Another slightly different way to do this achievement is to play a Warfare match in the Market District map with 1 godlike bot. When the match starts, grab the weapons from the rack and go to the north corner of the power core room (by the steel crates). The bot will capture the prime node and then come and attack your core, select the Flak Cannon and approach from behind and blow the bot away. Make sure you are in the north of the room "hiding" by the crates, the bot will focus on attacking the core rather than taking care of you. Keep repeating this until your core is destroyed.

One problem I encountered is the bot will sometimes just hang around his power core, as if it's bugged .... to fix this just grab your orb and capture the prime node and hoverboard back to the hiding place. This will wake him up and he'll either grab his orb or attack the prime node.

By doing this method over the 2 battles required for a default Warfare match win you should reach the 20 kills required without dying. One thing to note, the achievement didn't unlock for me when I reached the 20 kills in game, it unlocked after my power core was destroyed for the second time and the final score table was displayed.