Without the time of birth one can say very little, because the time of birth configures all of the 12 houses of the chart. The houses reflect ones experience in material reality. The sun in the 1st house in Libra is vastly different than the sun in the 12th house in Libra, to use a simplistic example.
But yes, a careful analysis of a natal chart that includes an accurate birth time and place of birth would very precisely determine someones personality. It could also determine the personalities of the parents, indicate the nature of partners and friends, health, the home and work environment and just about anything else you can think of. Not in precise specific detail (though one _can_ get specific), but thematically. And further, one can project this chart forward through time to determine future events involving said themes, also with great accuracy.
Unfortunately however, the weakest link in astrology is the astrologer, as has been said time and again. It requires extraordinary skill and learning gained through years of study, like any technical craft.