Do the indulgences granted for praying the rosary require that all of the mysteries are prayed?

Only five decades of the rosary are necessary for gaining a partial or plenary indulgence. The Handbook of Indulgences states:

A plenary indulgence is granted when the rosary is recited in a church or oratory or when it is recited in a family, a religious community, or a pious association. A partial indulgence is granted for its recitation in all other circumstances.

It has become customary to call [one set of mysteries] the “rosary” also. Concerning this customary usage then, the following norms are given regards a plenary indulgence.

1. The recitation of [one set of mysteries] is sufficient for obtaining the plenary indulgence, but these five decades must be recited without interruption.
2. Devout meditation on the mysteries is to be added to the vocal prayer.
3. In its public recitation the mysteries must be announced in accord with approved local custom, but in its private recitation it is sufficient for the Christian faithful simply to join meditation on the mysteries to the vocal prayer.
4. In the Eastern Churches where recitation of the Marian rosary as a devotional practice is not found, the patriarchs can establish other prayers in honor of the blessed Virgin Mary which will have the same indulgences as those attached to the rosary, (e.g., in the Byzantine churches, the Akathist hymn, or the office Paraclisis). (79-80)

Keep in mind canon law concerning gaining indulgences:

To be capable of gaining indulgences, a person must be baptized, not excommunicated, and in the state of grace at least at the end of the prescribed works. To gain indulgences, however, a capable subject must have at least the general intention of acquiring them and must fulfill the enjoined works in the established time and the proper method, according to the tenor of the grant. (CIC 996 §1-2)

For additional information, see Pope Paul VI’s Apostolic Constitution on Indulgences (Indulgentiarum Doctrina).