Actually, any of the three possibilities you suggest are considered grammatically correct. The consideration that determines which is most appropriate to use involves the exact timeframe the speaker wishes to convey with the sentence.
The first sentence you present, "Live the life you have always imagined," is an example of present perfect tense - a condition that has been going on for some time in the past and is still happening at the time of the statement. The adverb "always" means the past time goes as far back as you remember (perhaps literally, perhaps figuratively).
Your second example, "Live the life you always imagined," is a simple example of past tense. At some time in the past you imagined how you wanted your life to be ("always" makes it at all times in the past); now you are being told to go and live in that manner.
Your last suggestion, "Live the life you have imagined," is also present perfect tense. It is the same as the first but without the defining adverb "always." You have thought about your life in the past and are now being told to do what you imagined.
So, any of the three sentences can be properly used. Your choice depends on what you wnat to say about your past imaginings. The evaluation of these setences relates to tense and aspect, important parts of English grammar.
Two other perfective aspects/tenses are present perfect continuous, which requires "have" plus an -ing particple, and past perfect, which requires "had." Each gives different relationships between the present comment and future or past events.