You can place the dummy next to the summoning stone and pity him for the achievement but there is no other way in. Just ask for someone that is about to log of to form a raid, but remember he needs to stay in your raid the whole time as you spawn alive after dying in naxx.

I had to find someone that needed the achievement too. Once they leave the group you can solo it.

Now that the trial version of WoW is permanent, you can level a trial character to 10 and just invite them to a raid group and then log off the trial account and the raid group will stay grouped.

You still need a raid group and there is only one instance door (technically 4), but no one else needs be in your raid while you kill kill kill.

Have a guildmate invite you to a group on one of your alts. Convert the group to a raid. Log off your alt, then log onto your hunter (or other support class that can solo). Have your guild mate invite you to the raid group and then make you the raid leader. Once you are the raid leader you can kick the group mate or they can drop group. Now you are in a raid consisting of you and your logged off alt. Have fun slaying internet dragons, or star clusters, or spiders, or whatever.

If there is a guildmate about to log off or log on to an alt you can just invite that player and then convert to raid. Once they log off then you are by yourself and their ghost of a character.

No, you have to be in a raid group. However, that other person doesn't have to be with you or even online.

I use my Dad's account for this. Raid group with a character, log him out, and then just go have fun.

You can form raid with your offline alt.
Just ask someone to stay in group with your alt, pass leader to this person, log off from this character, log onto your hunter, pst that person for invite and get leader back.
Say "Thanks!" and let that person go.
Now you can form raid with your offline toon :O)