The term "criminally insane" is not a legal term.
Holmes has offered to plead guilty to avoid the death penalty. But his attorneys believe he is mentally ill. If he is mentally ill, then there are two possible legal states. "Diminished capacity" has certain mitigating effects. "Legally insane" might mean that he was not competent to stand trial, or that he could not be found guilty (classically because he could not understand the moral significance of his acts, but the interactions between psychological diagnosis and the legal meaning of insanity have complicated this in the last few decades). This would usually be called "not guilty by reason of insanity." This status has created severe problems in other cases, such as serial killers being hospitalized, then released, then going off their meds and killing again.
Some states have a new category, "guilty but insane." I have not heard that this can apply in the case of the Colorado killings.
The offer of a guilty plea may be a negotiating tactic to avoid the death penalty. But if Holmes is mentally impaired, the court or the prosecutors may not accept such a plea, even if his attorneys offer it. If he is not mentally impaired, then he can enter any plea he wants. But in this case, he is not simply entering a plea, his legal team is proposing a plea bargain: "I'll say I'm guilty if you drop the death penalty." The prosecution doesn't have to accept this bargain, and is likely not to want to, as they have a very strong case against Holmes and, for those who believe in the death penalty, 24 (or more) counts of first degree murder is a pretty good reason to go for it.
Holmes's suicide attempts have been called "half-hearted." This complicates his diagnosis, at both the psychological and legal levels.
So we are looking at a complicated diagnosis combined with a legal tactic, not a clear admission of guilt by a clearly competent person.