The following are all the two star challenges added to the game
Dyin' Ain't Much of a Living
Kill members of NCR or Legion hit squads with weapons affected by the Cowboy perk. (Note: You do not need the Cowboy perk.
Even a God-King Can Bleed
Cripple Caesar's head with Throwing Spears.
Kill Caesar with a Knife or Combat Knife.
Kill Chairmen, White Gloves, or Omertas with any submachine gun, light machine gun, or minigun. (10 required)
Sic Semper Tyrannis
Kill President Kimball with any One-Handed Pistol.
Talk About Owned
Kill Benny with his own gun, Maria.
Vault 13's Revenge
Kill Super Mutants with 5.56mm Pistols, Plasma Defenders, Plasma Grenades, Power Fists, Rippers, or the Bozar. (15 required)
White Line Nightmare
Kill Fiends, Vipers, or Jackals with Tire Irons, Baseball Bats, Lead Pipes, Machetes, .44 Magnum Revolvers, or Sawed-Off Shotguns. (20 required)
Hit squads are enemies that appear once you upset either the Legion or NCR (not sure if both appear at the same time). They appear at certain locations and respawn after a few in game days. I'm not sure on the spawn locations for NCR but for Legion you can find them when you are near Cassidys Caravan Wreckage.
The following weapons are affected by the Cowboy perk. Weapons marked with HH are found in Honest Hearts and LR are found in Lonesome Road. Most of these can be found from weapons dealers like Gun Runners.
Fire bomb (HH)
Bowie knife (LR)
War club (HH)
.357 magnum revolver
.44 magnum revolver
Abilene Kid LE BB gun
La Longue Carabine
If you decide to cripple Caesar's head be sure to save prior if you are not interested in the ensuing fight. Throwing spears can be obtained with the Tribal pack of you have the pre-order or purchased the Courier's Stash DLC. Otherwise Mick & Ralphs occasionally sell them along with other merchants.
Killing Caesar with a knife might prove troublesome since a big fight will occur once you put your hands on Caesar. Unless you plan on killing everyone with the knife you might kill Caesar with another weapon. You can find a knife in Doc Mitchell's house or Combat knifes in the Vikki and Vance casino. If you plan on doing both Caesar challenges I suggest doing one before and these two afterwords so if you decide to reload the save you can complete the challenge and achievement.
For Nyeh! See? buy a trail carbine or Sleepytyme from Gun Runners and go to the Strip and kill all necessary enemies. If you don't want to kill the Chairmen, White Gloves or Omertas then save prior and complete it. Be warned it will need to be the final challenge or it won't count if you reload.
I don't recommend trying to kill Kimball with a pistol since it's late game quest and obviously a hellstorm of enemies will try to kill you as a result.
If you want to kill Benny with Maria then when you confront Benny shoot the weapon off his hand and pick it up before you he does. I suggest bring companions to even out this fight.
An easy supply of Super Mutants are the group in Jacobstown but unless you don't want them dead either save this for last and reload when done or kill the Nightkin for the quest Come Fly with Me or go to Black Mountain.
Enough Fiends for the challenge can be found near Vault 3. Several of the weapons needed for the kills can be easily found when attacked in Freeside. The guns can be found at Gun Runners as well.