Running it multiple times and noticing patterns.
Stack aoes pretty much always have the same aoe maker.
Multiple marks go out basically means spread out
Are you marked and tether to the boss? Run away
Giant dark looking eye or anything move with the words "Gaze" or "Stare" equals look away.
Stuff like that.

Also knowing the themes of each fights helps. Like realizing Ramuh ex has water so you know that at some point that will become conduit of electricity.
Then you can use word puns on moves like Lunar Dynamo from T9 and saying Lunar Donut.