There's really nothing else to it in my experience. In most of my WoW life I raided very casually, took me months to even get 10N Lich King or Sha of Fear dead. Then for ToT I decided to get invested in higher-end raiding, and joined a better guild, honed my skills and got cracking on min-maxing my character. SoO I was getting AOTC in the second month of the tier, and by BRF I got my first CE, even if very late in the tier as a benchwarmer, and now I have a permanent spot in a Mythic guild.
The part that sucks the most about climbing up is leaving old guilds behind, either due to them not fitting your ambitions or disbanding. But it's very unlikely that you'll find a middle of the pack Heroic guild that successfully transitions into a Mythic one; the climb in terms of skill, preparation, and dedication is just too steep sadly.