Hint - ID boss
You can only battle ID when you get the Weapons Room key from Citrine. ID is located in the CAT Testing Grounds on the E.V.S system. ID is a bit hard to defeat. Here is the best strategy I could come up with.

Before You Battle ID - I would wait to defeat ID until you get passed Abel's Ark (which has a boss battle I will be covering soon) so you can acquire Heaven's Door while you are at the CAT Testing Grounds. I also recommend buying about 80 Half Repairs, 50 All Repairs, and 99 Nano Repair Ms. Make sure all of your best E.S. equipment is equipped. You will also obtain Anima 3 when you defeat Abel's Ark, which will come in handy while battling ID.

Step One: When you first start battling ID, he is about as strong as an eleven year old. ID may seem like an easy boss at first, but once you are done defeating his first form, he will transform. You should not have any trouble defeating ID's first form. If you do, than there is no way you can beat his second form, even with help like this.

Step 2: ID's second form is the hard part. The following strategy was the one that worked best for me.

Unless the E.S. Asher is down and out, have him in the battle. The other E.S.s you have in the battle don't matter. The only thing you need to look for to decide which other E.S.s you should use is how much MAX Health it has. Sometimes there will be a blue arrow pointing to an E.S. which you can see once you use the E.S.s. If it is pointing at you, odds are, ID is going to beat the crap out of that E.S. Use the Guard command as the E.S. that the blue arrow is pointing to as that E.S.s turn.

Let the E.S. Asher be the only one to attack ID. Only use far distance attacks! Let the other E.S.s heal all the other E.S.s to keep you in the battle. Once the E.S. Asher has a full Anima guage, use his special attack. I would save the Anima you get until you have three full Anima guages.

ID will use an attack called Demon Lord if he starts to charge. You will get a heads up message when ID is charging. He will attack on his last turn. When he charges, I don't care if you have three full Anima guages, I don't care if the blue arrow is not pointing to you, YOU MUST BLOCK! Repeat this process until you defeat ID.

Hint - Defeat EK Sigma Easily
Erde Kaiser Sigma could easily defeated if you have Erde Kaiser, Erde Kaiser Fury & Dark Erde Kaiser ether. EK & EK Fury Control Device could be found in Segment Address on Elsa & Labyrinthos. I believe you can found both Address & Decoder easily.

While Dark EK Control Device could be found in Segment Adress #6 on Durandal Park, and the Decoder are from Omega ID. Now for the battle, get a defender like KOS-MOS OR Ziggy in your party, or have them both if you want. And spellcaster like MOMO. Equip your spellcaster with Heaven's Door.

Step One: When the battle starts, use KOS-MOS or Ziggy break tech. Have the caster cast beam ethers, and the other supporting caster & defender, while attacking sometimes.

Step Two: After some turns, Sigma will start using Kaiser Shield. This could be the hardest part if you don't have all EKs ethers. Here is the list of EKs ethers you must use to shut down each Kaiser Shield:
Kaiser Shield I - Use EK ether
Kaiser Shield II - Use EK Fury ether
Kaiser Shield III - Use Dark EK ether
Have your caster cast it all, and don't worry about EP consumption, since you use Heaven's Door all EP consumption is 1. After one shield is down, it will use another one. After another shield is on, don't waste your turn by doing anything useless.

Use EK ether that will destroy the shield before its next turn. This way it won't attack because it's too busy to cast shield on itself. And don' forget to attack with break techs.

Step Three: After you destroyed all three shield, it will vulnerable to any elemental attack. At this time, its break gauge must be high. Attack it a little more to get it break. At its break state, use all your strong elemental attack and Dark EK ether. If necessary, have all your party cast Dark EK, and use Ether Pack if you run out of EP. Keep using Dark EK ether, and after he recovered from break state, he may survived with some HP, so finish it before it start using deadly attacks.