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The reason you couldn't beat Adremmelech with a long Quickening Chain is because he uses Perfect Defense when he gets to 1/5 HP which makes him immune too all damage for about a minute. Most/all of the summons after Zalera take two or three Mist Charges and are equally as useless as the others. A viable strategy is almost always better than a Quickening Chain or an Esper.
Hint: Syphon to replenish MP rocks. Buy it at any airship
That is precisely what I liked about Espers / Summons: bring them out when you need something to kick butt for sure. I used them for that and my characters for all other battles.
Belias, Mateus, Adrammelech and Zalera takes one Mist Charge.
Shemhazai, Hashmal, Zeromus, Exodus and Cuchulainn take two Mist Charges.
Chaos, Famfrit, Ultima and Zodiark take three Mist Charges.
Espers are useless. I rather have my Vaan fighting alone than have someone that require me to heal him/her everytime.
The only Esper I like to use is Exodus because he's a Libran. :p
But I'm a completist, getting them all is a must. :D