Any criticism of Israel that is not based on the truth, the whole truth, and nothing but the truth, is not legitimate criticism.
There are other grounds on which to label criticism of Israel as illegitimate. However, it is important that any such ground hinge on a neutral criterion, that is one that doesn't depend on any viewpoint about the conflict and allow that any criticism that does pass some set of viewpoint-neutral criteria is actually legitimate. Any viewpoint-dependent criterion will be dismissed by anyone who does not share the intended viewpoint and only create excuses for those who wish to claim that we just hurl accusations of "antisemitism" in order to silence legitimate criticism. Fidelity to the truth is one such neutral criterion, one that everyone in the elite media claims to hold dear.
Ben-Dror Yemini provided an excellent resource in his book The Industry of Lies listing violations of the truth by those seeking to justify the demonization of Israel, so I will only provide a few examples. First would be violations of "truth." That would include lies, fabrications, and exaggerations. For instance, claiming that Israel perpetrated a massacre in Jenin during the Second Intifada would be propagating a lie. So would claiming that Israel is responsible for Gaza's flooding by opening dams in the Negev.
Violations of "the whole truth" would include suppression of relevant facts. For instance, it is popular among the western chattering class to denounce Benjamin Netanyahu as a racist. There is no use denying that there is legitimate evidence in support of that notion, such as his exhortations during past campaigns about Arabs turning out in droves to vote. However, comments like that have to be balanced against Netanyahu's support for increasing budget allocation to Arab towns in Israel. It is a legitimate opinion, albeit one that I reject, that the balance of Netanyahu's statements about the Arabs and his budgetary priorities indicate that he is a racist. However, the western media do not try convince the public of that. Rather, they make sure that only the minuscule portion of the public that reads Israel-specific media, and a few outliers like Gatestone Institute, know about any of the evidence contradicting the claim of Netanyahu's racism and are thus left with the obvious conclusion that Netanyahu is indeed racist. Such is a lie of omission.
Presently, it is fashionable to claim that knowing a snippet of the history and present of Israel's dealings with the Palestinians is sufficient to assess moral culpability. Attendant with this moral narcissism is a complete intellectual incuriosity for any facts that do not fit their neat narrative of a morality tale. Calling attacks on Jewish settlement of the core land of Jewish history (Judea, and to a lesser extent Samaria) as ipso facto illegitimate invites the simple rejoinder of "Why can't recognize that the Palestinians are human beings?" Focusing on the accuracy of claims made against Israel removes that response, forcing those defending the use of such criticism to argue either that the omitted facts are inaccurate or irrelevant. I have a hunch that Israel would be better served by such critics twisting themselves into pretzels to justify the exclusion of inconvenient facts than simply yelling louder that our entitlement to Judea and Samaria justifies any hardship imposed on the Arabs living there to a population that is at best skeptical of that notion.