I agree with shmunkster, the healer wasn't good enough or the team wasn't geared enough overall.

I guess you could have the tank limit break right after Titan's heart is shattered to give the team a defense buff, but if you have less than a 50% success rate on getting past Titan's heart then I would do a DPS limit break. Since you are one of the single target limit break jobs (monk and dragoon), you or a dragoon should do the limit break to be most effective.

Zooming the camera out is kind of a joke because Yoshida said that's why people struggle with Titan hard mode and not lag, but you should seriously ask everyone to zoom their camera out. It makes night and day difference basically. I regrettably ate a lot of damage as a tank my first time on Titan because I was zoomed in really far and couldn't see Titan's moves. Keep practicing and try with different groups if a group doesn't work out for 20 minutes or more.