Resumiendo en ocasiones no salta a las 150, pero lo obtendras a las 170+.

Unlock 150 Dog Tag displays
Go into "Operative Status" in the multiplayer menu and then go down to "Dog Tags." The first tab "General'" has 64 Dog Tags which DO count towards this trophy. The combined other 3 tabs "Mystery," "Medals," and "Awards" total 64 x 3 = 192, making 256 total Dog Tags. Unlock 86 more Dog Tags to get this trophy. The Mystery Dog Tags are obtained by ranking up and obtaining unlock points, so when you hit level 50 you will have all mystery dogtag unlock points (128 Dogtags total, meaning you only need 32 more). The "medals" and "awards" Dog Tags must be attained through accomplishing hidden tasks and match awards respectively. This trophy has been mildly reported as glitching (not popping @ 150 dog tags), but does pop at 170+ for those who did not get it @ 150. So just keep earning unique tags and it will come.

For a work-in-progress list of Dog Tags, see here:
Partial Dog Tag List - Credit to Jumnious from Xbox360Achievements.org for the list.

Besos