I don't see it as a PS3 problem. My boyfriend and I play on the same network and he has no issue dodging anything in the fight (I play on PC and he plays on PS3). What is more likely the issue is...

1) Your ISP down/up speed is too low. When I first tried Titan hard, I was getting hit by everything, landslide included. I upgraded to the next level and have had zero issues dodging ever since -- extreme modes included. Granted, I have played many MMOs and never had ANY issue with latency or a need to upgrade my ISP package until this game... so that is a little weird. I'm fairly close to the NA datacenter to boot. (I'm in NY and Montreal is about a 8-10 hour drive away.)
2) Your ISP is not choosing the most optimal 'route' to get to the datacenter, thus increasing your ping more than it should. People use all sorts of programs to 'force' themselves to choose the fastest, most reliable route. I'm not sure if this is an option for the PS3.
3) You are experiencing graphical lag and just not seeing stuff in time to realistically avoid it. I would suggest lowering some of your settings on your PS3, especially if it is a bit old. My boyfriend had to lower some settings (remove party effects) to be able to see AoEs reliably. Keep in mind that the PS3 is a very old system. If FFXIV does not run well on it, it is because the hardware can't handle it... not because the game wasn't made well. The graphics quality of FFXIV on PC is much, much smoother than PS3.
4) The servers, in general, are notoriously laggy right now. People who are pro dodgers for an hour of progression will suddenly die to every plume and get hit by most landslides. I believe them when they say they are lagging because I witnessed them dodge like pros for a long time and then suddenly they can't? Not a player issue unless they are just getting tired... but I've been in runs where everyone dodges like pros and then 2-3 people start getting hit by EVERYTHING. One lag spike can and does kill you in this fight... and one death or landslide can mean the difference between victory and defeat.