So...have you ever wonder where did ppl get those other eidolons that you dont have yet and how did can i obtain one? Well worry no more i'll explain (and maybe others can help out too).
Click this link -> https://www.youtube.com/watch?v=11Ld90uTEqw&feature=youtu.be
How to get Eidolon: 1st: you need 75 Eidolon crystals (can be found in dungeons) or brought from players
2nd: Combine them (for this you will need 75 crystals and 1 hero emblem and also 5 gold
3rd: use Unidentified item
4th Go to the location that the "Call" tells you to. Like with my Sirgun, it told me to go to Helonia Coast (location should be on call or u can just right click it to auto move).
5th: After you summon it you kill it (should be done with a party even if your really good it takes time to solo)
6th: In a few seconds you should get mail that holds a box, obtain the box and open it. Beware tho, you only have a chance to obtain a key fragment (these cannot be traded so dont ask to buy them, some dungeons hold eidolons which drop those keys)
This wasnt in the video but, i will still expain....
7th: After you obtain the key fragment you will need 10 of them to make a solid key which holds the eidolon. But you will also need some other materials too like for example 20 medium experience crystals. After you make key you have yourself a new eidolon.
(if i didnt do a good job someone else can help me out O.o and i can edit this)