I already completed FC5 awhile back and now I'm close to completing it for a second time. I found the capture missions to be fairly difficult at times but not impossible and certainly easier than a couple of the Clutch Nixon missions.
Anyway, yesterday I was doing "Only You" - and having a bit of trouble, then I decided to try something different and that's what made me complete it the very first time with this new strategy.
Is it a glitch? Maybe. Maybe not!
This is what I did.
Instead of picking up the gun and killing the two guys at the start, I performed takedowns on both and then used the same strategy on the enemies I couldn't avoid in the mazy corridor section. I then noticed that the timer hadn't started. I paused the game and thought about what to do next. I guessed that the timer was going to begin the moment I picked up a gun but it didn't happen.
After the mazy corridors I headed directly for the far exit jumping over everything ignoring the enemies to the left and right of me and performing takedowns on enemies who came out of the entrance. I then picked up a gun knowing that the next parts would be too difficult to do without one. Like I said before, the timer hadn't started once I picked the gun up so completing the rest of the mission was going to be easy.