First playthrough I figured I would pick up all the companions towards the end since I didn't care much about them. I decided to go for them just before working the main quest line in New Vegas. Unfortunately it seems that all the quests I completed at Crimson Caravan and Camp McCarran somehow made it impossible for me to get Cass as a companion as the Caravan offered me no additional work and the doc at McCarran only said goodbye after completing his vault questline. So I to second playthrough to get the hardcoe mode trophy and immediately set off to get the companions. The third one I came to is Veronica and I quickly go through her responses without reading them as I believe I did the first time. Well it ends the conversation and she only leaves me with 1 reply, Goodbye. I figured that it was likely because I had no interaction with the brotherhood which I knew I had to come to later, so I went off continuing the story line and picking up the other companions. I later make my way into the brotherhood and go back to Veronica, but still only the same stupid 1 response option of goodbye. I just read today that if you say something negative about the brotherhood in the first conversation that she will not join you. [censored] GREAT! I assume that is what happened, and now I am once again screwed out of this trophy. I wish so badly I had picked this up for the PC so I could just hack it because its incredibly annoying the amount of work I would have to go through again to get them all.

Yeah, you should pay attenttion when talking to Veronica for the first time...

I got that trophy on my second playthrough, just side with NCR, pick up Cass, then dump her for Boone, then get the rest who are neutral.

Exactly. A quick look on the wiki could have saved you a few hours of frustration; I should know, I've made quite a few mistakes myself when I never looked it up first.