Unlikely that I'll go for this (not many options for L, I, or T), but there's an outside chance if I can get the more difficult achievements early on.
EDIT May 27: Done! Only had to start two games
M is for Middle-Earth: Shadow of Mordor - Lord and Master
I is for Injustice: Gods Among Us - Lucky Break
T is for Trueachievements - Budding Hound
R is for Rock Band 4 - Locked In
I is for The Incredible Adventures of Van Helsing - Escort Master
A is for Action Henk - Too funky for myself!
L is for Left 4 Dead 2 - PRICE CHOPPER
B is for Borderlands 2 - Definitely An Italian Plumber