Zabardast is a commonly used word in Urdu and Hindi, and is used for strong and loud things, mostly in positive sense. Zabardast would mean something powerful, though not vice-versa is necessary. Also, zabardasti which comes from the same root is often used for a negative meaning, conveying coercion.
Zindabaad is a word that is more or less same as the phrase 'Live Long.' It's comes from the root Zinda, that means alive.
So, Shandaar, Zabardast, Zindabaad is a cry that talks about something that is grand, magnificent, powerful, and remains so for a long time to be.