I love fighting Titan HM, I have been joining PUGs daily and beat him at least once every day since September. I'm currently working on the 10th relic on a different character becuase I already have all 9 relics on my main character. 6 of my 9 relics were purely PUG'd and the rest were from running it with my FC.

My advice is don't spend more than 20 minutes per group unless they are willing to replace the inexperienced players (providing you have joined a experienced and geared group). I help out random PUGs and Duty Finder Titan's everyday and I always tell the PUGs that I only have 20 minutes before joining. If the group is capable on beating Titan, it will more than likely to happen on the 2nd and 3rd try.

I would also observe every player to determine what can be improved and will make them aware before starting the next attempt. We will usually get the win right after depending on the execution, if the group seem to be improving I will stay longer than 20 minutes.