From google:
How to beat Aster Protoflorian
Aster Protoflorian is a boss that you will meet at the end of Gapra Whitehood; so far, this is probably the toughest boss you have faced especially as you only have Lightning and Hope.
Aster Protoflorian is very tough due to the large amounts of HP, but with a little patience and the right tactics, you will soon beat this boss.
Here is a general strategy to beat Aster Protoflorian:
Stock up on potions to avoid having to switch paradigms too much - with a nice supply of potions, you can concentrate on staggering Aster. Once you stagger Aster you want to do as much damage as possible, so having potions becomes important if you want to concentrate on attacking and blitzing.
Be defensive early on – set up your buffs early, these will allow you to absorb attacks; then switch to healing for a while - watch the boss especially when it changes form – try and spot color changes it may become weak to some elements. If you can, detect these weaknesses quickly so you can concentrate on them.
When the color change happens use Libra – the AI controlled member will then attack with the correct weak element that you have detected.
When attacking use slash and burn paradigm ; try and fill the chain gauge.
While chain gauge is low, use healing potions – at some point perhaps 60% through the chain gauge, conserve potions and switch to a healing paradigm – be careful though the chain gauge takes a long time to fill, don’t make yourself start again!
Once the Aster Protoflorian is staggered the best option is to use launch – double cast to do more damage, and use potions to heal.
Don’t let your HP slip too low – you could die in a single powerful stroke.