We (Piper and myself) went in a Hazard Suit. Deathclaws, Ghouls and Bloatflies were a little bit of a problem and cost me ~200 shotgun shells.

http://staticdelivery.nexusmods.com/images/1151/9434437-1451939533.jpg

On later levels the Deathskull Radscorpions were fairly numerous.

Honestly I couldn't be assed to do it legibly so I got a mod that never drains fusion cores for power armor, got in my T-60 and brought along my gatling laser. I saw a streamer do it entirely by just dosing out on rad-x and radaway.

Power Armor does the job.

Otherwise, Hazmat Suit.

I've been getting ready for that part of the game. I have about 110 each of rad x and rad away and a hazmat suit. Can't stand power armor. Don't like it.