You have to independently determine if the "may" is necessary in each part of the sentence. As you know, "may" implies that an event is not certain, so only you can say (based on the context) if both events are uncertain. For example:
Due to the morning fog we may not see the sunrise, but we will see the sunset.
Due to the evening fog we will see the sunrise, but we may not see the sunset.
Due to the fog we may not see the sunrise, and we may not see the sunset.
Because of the ambiguity it's not always correct to omit a repeating "may", unless the meaning is obvious:
Due to the fog we may not see the sunrise, or the sunset.
In your example, if you want to emphasize that both are possible events, and not certain, there's nothing wrong with repeating "may". If brevity is your goal, you can, however, omit "it" from the second part, as the subject is the same, and also use "their" instead of "the victims'".
Robbery may not only take international students' possessions by an unlawful force, but may also endanger their lives.
As others have said, "may" is not really necessary in the first part, because it is a statement of fact, not conjecture. Using "may" only in the second part implies it is less likely than the first part:
Robbery takes international students' possessions by an unlawful force, and may also endanger their lives.
Of course, this makes the tone somewhat more ominous. It all depends on what you wish to say.