Without the use of mods, in New Vegas you can have one Humanoid (Human/ghoul/super mutant) companion, and one of either Rex or Ed-E (robot companions).
There are several mods that increase the companion limit.
In addition, you can gain temporary companions through the use of items like the NCR emergency radio.
The way of the hardcore is not easy or quick, but you can be the one to conquer it with just a few simple steps.
On water: You should devote as much space as you need to water, both purified and dirty. this will give you the stamina necessary to accomplish your quests with out the bouncing out to drink from the rad free sources convientiently located around the map. The best of these are Good Springs Source, the camp in the far south where you get Rose, and the NCR tenant farm. Also, remember that even an irradated source will reset you to zero so drink when you can to save bottles for when you can't.
On food: You should be able to scavange more than enough food from those you kill through the quests and just laying around to never even need to touch a campfire. Concentrate on things that have a high food to weight value like the squrriel-on-a-stick and the brahmin steak. I would recommend not using food to heal as the hit points aren't worth it on a weight basis, although if your hurt and hungry, they are a nice bonus.
On healing: Med supplies still don't have weight so get those! I also like to use soda but only when I have a ready source of water (irradiated or not). The sunsets are a better option than the nukas but dealers choice. I would save your stimpacks for your companions as they have a tendancy to drop quickly if it ever drops in the pot with things that are over your level. (As your speed running, your level will still be low at the end of the game).
On storage: I wouldn't worry about it. You take what you need along with you and leave the rest behind with out a backward glance. The fallout games make you want to be hoarder, but those guys smell funny and you don't even get be on T.V. so don't do it!
On quests: The trick with the quest is do the main plot and the ones you can do along the way. That's it. You can beat the game by the quickest method at level 24 or 25 as long as you don't do any of the long trek quests. You can also keep all the various factions off you until you have already gotten a bunch of fast travel spots in the strategic spots, which will save you time in the long run. To this end skip the Booted! quest as you don't want to have to run and gun all those assassins.
On companions: Boone and Ed-e, 'Nuff said.
On ammo: Ammo is a great way to make money, it's by far the lightest trade good in the game. I would suggest picking what you are going to use as a weapon and keep only that ammo and sell the rest. This also lets you ignore 3 skills entirely so that you boost your chosen skill even quicker. I would also grab the best gun for your skill even if it makes you go out of your way. That machine is a great choice if you're focusing on guns and there is a great energy gun in the factory just south of new vegas, if you'd rather go that way.
On the end game: This contains some spoilers so don't read it if that's going to upset you, kthxbye
The easiest and quickest path to the
end of the game is the Mr. House path.
It has the fewest hoops to jump
through and least amount of exposure
to inevitable pissed off other
factions. If you drive to the end
along this path you can hit the end at
an extremely low level, especially if
you invest in a higher speech.
Anyway, hope this helps you get that last little achievement with a quickness :)
Best Answer
Other than raising some survival for more water and food effects, the game basically plays the same. The 'hardcore' portion means only couple things:
At the end of the day, you'll simply fast travel to your base, usually Goodsprings with multiple external containers, mail box, workbench, nearby camp site with bed, rad free water source, and restock.
Sleep, eat, drink, restock, and then you are off.