Not only have people completed this challenge, but people have completed this challenge and all the requirements for getting the Order of Ambrosia rank except being at level 50. There are some really crazy people that have even done a 1-2-3 NLG challenge (no liscense grid), and succeded in beating every boss except the Undying (and that might have been accomplished by now). This involves a whole lot (and I mean a whole lot) of mote farming and Dark Matter charging. I am considering a 1-2-3 challenge at some point, but there's no way in hell I'm doing a 1-2-3 NLG challenge.
The basic concept of damage in this challenge is that guns don't base their damage on level, monster defense or strength/magic. The only thing that matters with a gun is its atk power (measures also work this way but are way to weak for use here). The most powerful gun, the Fomalhaut, is not difficult to get 6 copies of. The main problem (not in the least the only problem, just the main problem) with this challenge is getting to the point where you can get some Fomalhauts.
Edit: Most light armor gives additional HP to the character. While heavy armor usually has more defense, at level 1 more defense won't save you with 200 HP (or however much they might have). You can get as much as 1600 more HP from light armor. Add that to the HP you get from liscenses, and you'll have a decent amount of HP.