Surprisingly, it is possible to do that - unlike its lackluster sequel, "Fallout" has both preprogrammed 'backdoors' and exploit tricks that allow you to win without having to engage in a dangerous combat.
I wanted to put a link to my complete walkthrough, but it seems that "www.duckandcover.net" is still recovering from moving their site to another service provider, so just a few general hints:
- Don't touch combat skills. Increase 'Outdoorsman', 'Speech', 'Stealth', 'Science', 'Repair', 'Lockpick' instead. Charisma, Intelligence, and Agility (you'll need to run really fast) are A MUST!
- In random encounters - run.
- Use stealth in dangerous areas, and go in there at NIGHT, when enemies are less likely to see you (they have lower Perception at night).
- If you really need an item and NPC is not giving it to you, before attempting to steal it use at least 3 booze/whiskey bottles on him - it'll lower his Perception and help you in your stealing exploits.
- This is cheating, but you can cause SuperStimpack overdose that'll kill the NPC without giving you a notch in 'Kills'. Not that I approve of it ;-)
- Don't have any followers! They will not run from random encounters, and their kills will be considered yours!
More specific hints:
*** SPOILERS ***
- "Stealth Boy" does not seem to help you in sneaking. Correct me if I'm wrong, but nobody really knows how the damn thing works.
- To get XP for helping Killian dispatch the assassin sent to kill him, you don't have to kill the assassin - just hit him a couple of times then stand aside to let the guards finish the work.
- To get past Harry in the Necropolis, either try to outsmart him, flirt with him (if you're a girl), or sneak past him, in 'combat' mode if necessary (combat mode sneaks are cheating because no scripts run in combat mode).
- Purple robe will help you in the Cathederal and in the Military Base - this way mutants will not recognize you.
- Do not ask for assistance with Military Base from the Brotherhood - you'll get itchy-fingered Paladins that you don't need anyway.
- To destroy the Master, you can a) activate the nuclear device with a key you found at Leutenant's locker in Military Base, or b) convince the Master that his plan is insane by showing him Vree's autopsy report, he'll detonate the bomb himself.