I bought irl or received help to grind about 6 of my 100 mounts (see my collection). The rest I got on my own, per my guide. Instead of buying or grinding those 6, I could have gotten any combination of the following: 3 more Argent mounts, 1 Time-Lost Drake, 1 motorcycle, 1 Oracles drop, 4 holiday mounts, 1 Oculus drop, tailoring, or engineering.
Thus, this is not impossible to solo, and I've proven it. Birdfall has 1 other player to force to do stuff (husband), and she only got his help with the Ahn'Qiraj grind. She did almost all of this in level 80 5-man heroic gear and 1 fancy emblem cape.
You can do this.
I'm going to continue grinding mounts for Cataclysm in case they give us a new "Get more mounts for this achievement!" thing. It's not like I have anything better to do until the expansion. *shrug*
The outfit above is one of my RP sets.
The swords and cloak are from Baron Rivendare. The belt is off one of the Stratholme mini-bosses that you have to kill anyway to get to Rivendare.
The pants are Starfire Trousers, easily found on the AH.
The boots are simple Recruit's Boots, buyable inside Old Hillsbrad Foothills or swipe-able from level 1 human, dwarf, and gnome warriors.