Players were reporting tracking issues with achievements such as Recruit, Soldier, and Veteran, which require you to kill 250, 1,000, and 2,000 enemies across the three games, and Bruiser, which asks you to 'kill 100 enemies with melee attacks in Mass Effect 1, 2 or 3.' For most players, these should now be fixed, but some early reports from users in our forum suggest that may not be the case. There are numerous cumulative achievements relating to kills in the Legendary Edition, but it looks like the buggy achievements are ones awarded for killing a specific number of enemies across all three games.
According to the patch notes, the update 'fixes an issue where kills for achievements weren't tracking correctly' in both Mass Effect and Mass Effect 3.