[ShadowcatX]

Part of that goes to play style as well I think. Playing aggressively (including buying aggressively) seems to be very important in this game.

[Lord Cameron]

Further, you aren't restricted to applying that damage to a single obstacle either.   You play all the cards you want, from your hand, your friends play their cards as warranted, and all that damage goes into one giant pool that you can apply anywhere you want, in any order.

Not quite.  Damage is pooled per obstacle, based on what cards you played on each one.  Here is a thread where SevenSpirits (Sean McCarthy) explains it best:
http://www.boardgamegeek.com/article/16904516#16904516

Is there an official clarification from Catalyst on their website?
Because the article on BGG is great, but isn't considered official unless it's posted by the line developer or Catalyst...

I would suggest that you take a look at the upgrade giving you one extra card in your beginning hand at the start of the game. It is really useful to quickly defeat the first wave of ennemies so you can advance to the following scenes/rounds with less damage and less cards in the crossfire discard. Good luck in your games.

The selection of obstacles drawn on the first round are critical!
If your group draws cards like Ork Fixer, Corporate Adept, and Gutter Punks things will go well.
If your first draw is all tough cards like Aerial Combat Drone, Elf Shaman, Demolitions Expert, Merc Elf Decker etc then you will likely be down to a couple of hit points and with Crossfire level 2 or 3 by the time you finish the fist set of obstacles. With two more tough scenes to go and drawing mostly Hard Obstacles your chance of success plummets..

[Jamelfr]

Well Sean is a developper of the game. So you can consider his answers as official, both on BGG or here (his nick is Seven Spirits).

[witchdoctor]

I know our group has played it a few times and a lot of it is related to the RNG and what obstacles you draw to start, you get an obstacle with a huge or expensive damage track when you have no cards to play you are not going to have a good time.

[iduno]

Being aggressive helps a lot, and so does using attacks with the assist option. I also like prioritize attacks against any obstacle I can take down before it can attack. The first one or two characters will usually take damage, unless they get a weak opponent and a strong hand, so focus on damage you can actually prevent instead of having a lot of half-damage opponents (unless someone else will take them down soon).

There is also no penalty for becoming staggered, healing, and becoming staggered again. There are actually 2 upgrades (shock frills and one that gets you an extra card when you get healed from staggered) that make it a useful tactic. Hopefully it doesn't happen enough to make it worth taking those upgrades, but the 4 games I've played in were all close wins and at least one character was staggered (never critical) every time.