The thing is, enemies going hostile shouldn't mess up your Foxiest run. In order to get the trophy you have to earn the "Smooth Operator" experience bonus on every objective where it's applicable. All of these objectives are similar in that there are alarms that can be triggered by the enemy, either by an individual running up to an alarm panel on the wall or by a camera / turret / robot / lasers. Enemies seeing you and going hostile doesn't actually affect the Smooth Operator bonus at all as long as you take them down before they set off an alarm. I honestly don't remember setting off a single alarm, and I don't even remember an enemy being alive for more than a second after spotting me. I just don't know where I went wrong. The only thing I can think of is maybe a turret spotted me for a split second and went hostile and I just didn't notice or something.
The next time I do the run I'll go as stealthily as possible and I probably won't even worry about the guards. The only reason I did this time is because I was going for other trophies simultaneously. Also, to make sure that I get it right, I'm going to watch carefully and look for the Smooth Operator bonus after every objective where it applies. If I don't see it I'll reload and try again.