The Impossible Trinity achievement is absent in The Lost and Damned, but returns in the Ballad of Gay Tony with a different name: "Diamonds Forever".
The "Diamonds Forever" achievement is an obvious reference to the James Bond film Diamonds Are Forever.
In some cases, The "Impossible Trinity" achievement is not awarded. There is no known reason for this other than a glitch in the game or your system. Should this happen you must restart the game and play through until you get the achievement.