The phrase "tightly antonyms" isn't grammatically correct in a typical usage. "Tightly" is an adverb, for example, in sentences like "He held the rope tightly" (meaning in a firm or close way).
When we talk about antonyms (words with opposite meanings), we usually refer to nouns or adjectives having counterparts with opposite senses. For "tightly", the correct antonym as an adverb is "loosely". For instance, if one sentence is "The lid was screwed on tightly", the opposite would be "The lid was screwed on loosely".
If you meant to ask about the antonyms in general, you should use a more appropriate word or phrase like "What are the antonyms of the word related to 'tightly'?" or simply say "What is the antonym of 'tightly'?" to make the query clear and grammatically correct in English.