At the Logismos Temple Top, is there any easier way to beat the Doom Eye?

I won by losing and then when ask if I wanted to load+high level I chose it. I started again with five more level and I win.

Learn to use Selan well. Have her throw her blade and spin it around the enemy without actually running into it.
If you do it right, it will deal lots of damage in a short time, and if you don't end it early, she will regain the IP cost by the time the attack ends. All you have to do is be careful not to be in front of it when it attacks.

Honestly, I never got why people say Selan was weaker than Dekar in the DS game. I took her to the Ancient Cave and had her solo the entire thing without dying once.

For that, buff her Intelligence and Magic Attack, then spam her Ice attack.
When possible, arrange her Mystic tiles so that she gets Rush, and any kind of "Enemies easier to knock down/knock back" tiles you can reach.

Done well, any enemy that doesn't have really high Ice resist will be killed easily, and you can use the Blaze Ring's Fire 2 for anything else.
When you're not in the ancient cave, use non-blue mystic tiles to empower your blue ones (those are the only ones that matter, anyways) and make sure that before you leave the Ancient Cave on incomplete runs, you sell all of your non-blue equipment and use the money and non-blue tiles to improve your blue ones.