So, in my first playthrough, even though I got the Boomers to side with the NCR, I COMPLETELY MISSED THE BOMBING RUN ON THE LEGION! I simply assumed the artillery shells flying overhead was their help! And since I had mistakenly installed Hardin as the Elder, I couldn't get them to help out the NCR. I was also too lazy to finish Arcade's quest, as I couldn't seem to get it to trigger.

So, in order to make the final battle on my second run through for the NCR more epic, what all should I do early on? I'm not going install Hardin as the Elder, and I'm going to make it a point to finish as many companion quests as I can. Other suggestions?

Also as a side note, from what I understand, the factions that will really side with you during the actual battle are the Boomers, the Remnants, and the BoS, correct? You should have been able to land aid from the Bright Brotherhood and the Super Mutants as well.

Yes.
I fought through with Enclave Remnants, Elite NCR and BoS together, side-by-side at my back... it was glorious, none could stand before us.
Actually, I don't think you see The Boomers fly over - you're much too busy working for the NCR.
It might be time for you to take control of Vegas for yourself, friend...
When I did YesMan, that's when I first saw The Boomers myself. Sweet!

No... not so much. (?) Guys correct me if I'm wrong,
Regards

You can also enlist Khans to help NCR, all you need is to kill Papa Khan to put Regis in charge.

I think it depends if you're rushing through or what. I know I saw the Bomber fly overhead at one point, but I'm pretty methodical and like to enjoy ripping people apart on the dam. The bomber flies overhead, drops a bunch of shells, a few Legion die or are injured from it... it's pretty fun.

The Bomber was so EPIC. It was then when I knew NV was one of the best games ever.

It was.