According to Google's dictionary, this is the definition of an idealist:
A person who is guided more by ideals than by practical considerations.
What, then, are Gatsby's ideals? Certainly Daisy is at the top of his list. In reality, Daisy is a married woman and a mother. She enjoys the life of high society, and Tom has provided this for her. Most compellingly, Daisy has already proven to Gatsby that she cannot be loyal to him. While waiting for him to return from war, Daisy made some practical decisions of her own:
She wanted her life shaped now, immediately—and the decision must be made by some force—of love, of money, of unquestionable practicality—that was close at hand.
In spite of already being rejected once, and in spite of the overwhelming evidence that Daisy has created the life of her desires (though an imperfect one by any standards), Gatsby sets out to win her heart. In order to earn enough money to impress Daisy, Gatsby dips into illegal means of income. He purchases a mansion, hosts lavish parties every weekend, and uses Nick as a means of getting closer to the girl of his dreams.
But that's all Daisy is—a dream. Gatsby is blind to the reality of the situation, which is that Daisy was never truly his to claim. She has moved on without him, and this is so eloquently captured in the scene after Myrtle's death when Nick catches a glimpse of Tom and Daisy inside their home together:
Daisy and Tom were sitting opposite each other at the kitchen table with a plate of cold fried chicken between them and two bottles of ale. He was talking intently across the table at her and in his earnestness his hand had fallen upon and covered her own. Once in a while she looked up at him and nodded in agreement.
They weren’t happy, and neither of them had touched the chicken or the ale—and yet they weren’t unhappy either. There was an unmistakable air of natural intimacy about the picture and anybody would have said that they were conspiring together...
Interestingly, it's not Gatsby himself who witnesses this intimate scene, symbolizing again his blindness to Daisy's reality.
Gatsby has equated his loss of Daisy to being totally dependent on his earlier lack of fortune. In his idealistic perception, if he could just overcome this hurdle, Daisy would return to him. Unfortunately, simply acquiring wealth isn't the sole barrier between Gatsby and the girl he lost years before, and he ultimately loses his own life because he cannot see that Daisy will never be his.