BigBigFan said:
You're only as good as your teams weakest link.
QFT. Similar to sports, a really great lone wolf can't win a game alone. This is separate from improving as an individual, but teamwork is crucial in competitive Halo.
Since the OP wasn't really asking this question, I'll just throw in some tips for players who really are wondering.
Precision weapons dominate in Halo; only power weapons can trump them. Find which one suits you best; the DMR suits most situations the best, but I use the BR the most. Headshots instantly kill when the shields are down, so watch for that pop, and go for the head. This is why I like the BR; it's very easy to nail that headshot at mid-range with it due to the burst fire.
Think strategically; try to use combinations such as a grenade to pop shields followed by a headshot with a precision weapon. Mind the maps, and use what's appropriate for each niche.
If you find yourself dying in a similar fashion a lot, learn from your mistakes. Strategies that work on lesser-skilled players might not work on others, and if you're dying to the same sniper many times consecutively, try another route to flank him.
Pick your battles; if you're getting plinked down from afar, run for cover. This can apply to closer engagements as well, and you want to be wily if someone gets the jump on you. This ties in with minding the maps, and if you're know exactly where you're at and what your options are, you can turn the fight around. Here's a scenario: somebody is trailing you on Haven; they have your health low and you haven't even hurt them. You're close to the elbow, and you sprint up it, throw a 'nade that pops the pursuer's shields, then quickly kill them with a headshot.