Soloable by patient rogues, as well as druids. For rogues, it's a matter of, well, patience, and for druids it's more of a test of gear. There are two packs of soloable myrmidons (two in each pack), as well as one killable patrol with two myrmidons and a caster however that one is very risky.
For rogues, if you have a dodge set, use it. Having preparation helps, and considering AR/prep is flavor of the day, chances are you do. Shadowstep rogues can solo this (I've done it as shadowstep) - however, you'll be using cheat death a good deal to make up for lack of DPS.
For druids, feral is really the only way to go. You can try doing this as mookin, but two elites on you hitting for about 400 per hit (vs moonkin armor) will whittle you down pretty fast. They have 20k HP each, and you have no vanish, so you'll have some trouble. Feral druids, do not use a cat DPS set. Try your best to whittle them down; your health can get low on two-packs, but you can always cyclone heal.
Pack one: sitting at the gate into the tunnel. Stealth around the side opposite the bog lords when you zone in (they see stealth), turn to your right, and you're looking right at them. Only thing to worry about is the patrol inside the tunnel.
Pack two: patrol in the big open room that leads to the last two bosses. There's two myrmidons (one on each side) and a caster in the middle. If you do end up wanting to fight them, the best position is to do it nearer to the last boss, so you don't get ambushed by any stray mobs.
Pack three: on the way to the second boss, just before the tunnel with slaves, a pack of two. Nothing to worry about.
Rogue strategy: sap one, kill the other. Unless you have stellar gear, you won't kill it until after sap wears; I would suggest saving evasion as much as you can. Worst case (you get crit a lot), you can vanish and wait it out, or prep evasion (I wouldn't suggest this - 14 mobs is a lot to kill, and prep can be a great timesaver.) Abuse your blind as well; you can get a 55 second sap by blinding as sap fades, buying you extra time. Another nice use of blind is, while sap is still in effect, to blind the mob you're killing and bandage. Generally, after you kill one, you can vanish, re-sap, eat, and then engage - if you have evasion again (i.e. you're combat and you have the lesser cooldown) use it, if your gear isn't great you'll probably want to wait for it's CD to be up.
Feral druid strategy: open on one of the mobs in cat, and get a few good swings in. As the other mob approaches (which will be nearly instant), shift to bear and let the whittling begin. You won't have any lack of rage with two mobs hitting you, so feel free to spam swipe and pop frenzied rejuv relatively early in the fight. Once that heal wears, hopefully your health won't be too low to bash, shift out and heal. There will still be one mob hitting you, so your only choice may be to rejuv and shift back. Otherwise, just regrowth rejuv and go back into bear. Another possible strategy would be to bash, cyclone, and get in a more satisfying heal, but you will get hit once or twice more in the caster interim. Once the first mob is dead, the second one is easy going; feel free to cat DPS to speed things up, but don't get too low. Against cat the mobs hit around 1000 per smack, and they also have a cleave. Safest bet would be to heal yourself to full when the first mob is dead, and then continue the beardom for the second.
I don't think feral druids can solo the three pack patrol. Without any effective, long term CC, you're really SOL. For prep rogues though, the option is there - you'll need pretty good gear to mitigate damage but also DPS fast enough to kill them though.
The two methods of killing this patrol - sap the caster, and use your normal method of killing, but evasion early and prep evasion soon afterwards, abusing blind afterwards or between the two evasions. You can also sap one myrmidon and kill the other while trying to mitigate the caster damage - evasion doesn't help, or sap one myrmidon and rush down the caster ASAP. Either way, you will definitely need to vanish after killing one to refresh your CC and your HP, and probably wait for evasion again.
No matter what though, it's probably smartest to get a SV group for this. 14 mob kills is a lot, and for a well-geared prep rogue to solo it still takes about two hours to kill the mobs. It's dangerous, and while you get all the armaments that drop, it's still more time-efficient and profitable to take the full run.
... however, if you're a rogue with a druid friend (or vice versa), then go ahead. The druid can heal and add DPS, and you can get down all six mobs per run, completing the entire daily in under an hour.