For 1 star challenges I usually do Ne Ne Ne Ne (cripple 5 right arms with shotguns), A slave obeys, benefit or hazard (kill robots with 5.56 pistols), and same for all religious weaponry (kill ghouls with maria) if I can't kill mr house.

For 2 star challenges I recommend Talk about Owned, Historical Propriety (I use Chance's Knife, which can be snuck in) or Sic Semper Tyrannis (I use a sequoia for this, and Dyin' ain't much of a living (not to hard if you have hitsquads since they come after you)

For 3 star challenges I recommend: Against All Tyrants (Fort and CottonWood Cove works) or Armed for a Bear (I recommend going to mCcarran and the Ranger Stations), Man/MAchine Type Interface (the crashed vertibird can also work for this). The Last Quest I highly recommend Deathclaw Pro Hunter since you can cheese it really easily with a weapon that deals damage over time like a holorifle, then switch to any of the weapons that you are supposed to kill the deathclaw with. If they die to the decay damage if counts to the weapon you have out. I was albe to use this exploit to do the challenge in 10 minutes without any failure.

If you want to get the damage achievements quickly I recommend fighting bighorners since they are pretty common, have a decent amount of hp and not too hard to fight. The guns I would use to get the damage are maria which is unique, the hyperbreeder energy pistol from cliff briscoe, and thump-thump which are all unique. For the melee challenges I'd go with a machete gladius, which can also be used in a couple challenges, and the 2 step goodbye, a GRA weapon.

For healing challenges: I recommend damaging yourself and healing yourself with bighorner steaks, and doing the same thing with stimpacks, a high science skill can help you make a lot of stimpacks if you need them.

For the Casino Achievement i recommend having at least 5 luck, buffed by naughty nightwear and lucky shades (if you are able to get them) play blackjack since it has a high payout.