There are two points in Mass Effect 1 where you can get this achievement:
Your first impossible situation is on Virmire with Wrex. When you try to destroy the potential cure for the genophage, Wrex will become angry. You must talk with him, and try to reason with him as to why the facility must be destroyed. Some of the old guides for the original game say 8 points in either charm or intimidate is enough, although I can not vouch for it, as I had max charm when I got here. If you have enough points, you will be able to talk him down from his stance, and he will agree to keep on fighting, which unlocks the achievement.
The second impossible situation is near the end of the game on the Citadel, when you can talk with Saren in the council chambers. After talking with him, you must convince him that he's become indoctrinated, and convince him to commit suicide.
Hope this helps.
Edit: According to @Triarius, getting Wrex the ancestral armor will also count towards this achievement in the event you do not have the required points in charm or intimidate.