Been getting a lot of experience at this fight over the last couple days and figured I'd share some tips and tricks I've picked up on. Most suggestions involve oldschool rote memorization of his patterns. That's probably the best way to do it, but if your memory isn't that good or you get nervous easily it may not be able to help you.
Tip#1: Zoom your camera all the way out. This has become a bit of a meme courtesy of SE, but it really will help you keep track of the happenings better.
Tip#2: Put Sprint and an instant ability of any kind on your #1 hotbar, on two of your right thumb buttons. If you get caught casting in the center of a plume, popping sprint very quickly can still get you out in time. Using an instant ability also forces the server to update your position. If you just dodged that landslide by a hair, it will probably hit you anyway due to the server's update lag. Pop that Instant as soon as you're clear so the server knows it missed you.
Tip#3: Whack him with normal melee attacks for a while when the fight first starts, until he uses the first Weight of the Land (plumes) attack. This builds up the Limit Meter. Having a level 2 Limit for use on the Heart phase will make the fight easier.
Tip#3: After Titan uses the first Geocrush (big AOE jumping stomp move) you can make your life easier if you start using a "stick and move" rotation. After every ability Titan uses, assume you have about 3 seconds before he either Landslides or Plumes. Cast a spell or use a CD and start moving pre-emptively. You don't have to memorize his whole pattern if you expect the AOE whammy after every move - keep moving and you'll dodge something, be it a plume or a Landslide.
Tip#4: Bombs go off in the order they drop. Sit by the last one til the first one goes off, then run to where the first one was. Wait for a second or two after it goes off so the server lag won't think you got hit running into its AOE. For the big bomb pattern that covers the whole field, just run to the edge as far from any of the bombs as you can get. Those spots are safe. He likes to throw a Landslide as the bombs are ticking down, to be prepared to dodge it on the way to your safe spot. Having your camera zoomed out makes seeing the bombs and incoming attacks much easier.
Tip#5: When Titan's Heart shows up, one party member will be stuck in a rock (Granite Gaol). Break that member out so he can help DD Titan's Heart. But please remember that a Healer needs to Esuna / Leeches him! The Granite Gaol gives you a massive, MASSIVE attack down debuff. If you don't remove it you almost may as well leave them dead. They'll be that weak. Titan will trap someone else in a rock just a few seconds before he Astral Flows you - ignore that person and break the heart. Once the heart is down, THEN break them out so they don't get oneshotted by the super move.
Tip#6: Throw everything and the kitchen sink at Titan's Heart! This is the biggest damage race I've ever seen. My last group literally came down to winning or losing based on my SMN. Rouse > Enkindle was just enough to push us over the damage limit. We broke the heart each time with a fraction of a second to spare. Save your big damage buffs like Berserk and Raging Strikes for this phase - heck, our MNK popped a Mega Potion of Strength - you need every measly point of dps you can get.
Tip#7: After the heart goes down, spread out along the edge of the small arena. That way everyone can run towards the center to dodge plumes instead of being boxed in by them. After you dodge, move back to the edge. Remember how to avoid the bombs.
Tip#8: Its a long fight, and slow and steady wins the race. After the heart, don't get in a hurry or start fumbling buttons. It's better to do no damage and just relax and dodge for a minute than it is to get hit and die. Don't get too excited, just focus on dodging and, as a secondary task, do a little dps when you can. You'll eventually grind him down.
Tip#8: Good gear helps with this fight a lot. It really isn't like the first two HM Primals, and I say that as someone who detests gearwhores. Before you try him, "make sure you've replaced all your AF with better stuff and gotten a weapon upgrade" is the best advice I can give. Wanderer's Palace is your friend for this I think. Do WP runs until you get your Darklight Weapon from the Tonberry King. By the time you have that, you'll probably have enough tomes for a couple pieces of Darklight Armor and/or accessories, and the WP gear drops (Warlocks Robe, etc.) in the rest of your slots. That's not adequate to farm Titan, mind you. But if you're going for the story/relic quest one-time-clear it is adequate to not be a burden. Farming Amdapor Keep for the gear that drops there and at least your Darklight Body and Legs, and your weapon drop from HM Ifrit is much better still. Personally I did it with a mishmash of Relic body, WP gear, DL accessories, and an Ifrit's weapon and didn't have much trouble once I got a party that was similarly geared and could dodge. I love my AF armor and you do too, but it just. isn't. enough. for Beating The Hard Fatty (BTHF - my LS's nickname for the fight). Make sure your HP is over 3200. 3400 is better, but 3200 is about the minimum you can survive his AOEs with. Less and you're not helping the fight because you'll spend the whole thing insta-dead. >:(
Tip#9 Final: Train for the fight a little. My LS came with me to do a few runs of Story Titan so I could sharpen my dodging skills on his Landslides. When I was confident I went ahead and flagged up Titan HM in the Duty Finder, not expecting to win. I did a couple dry runs like that just to get a feel for the fight (though we never got past the Heart). After that I did something else I never do - I watched a guide video for the fight on Youtube so I'd have an idea what to expect. Finally I joined a shout party in Revtoll on Sunday and we did 9 runs, getting past the heart several times and giving great experience for the fight. A second shout party cleared it on the 7th try last night before maintenance.