Here is the full list of all 16 GENIE Reprise achievements worth 1,000 gamerscore.
Begin Part I.
Begin Part II.
Begin Part III.
Begin Part IV.
Begin Part V.
Begin Part VI.
Begin Part VII.
Begin Part VIII.
Begin Part IX.
Begin Part X.
Begin Part XI.
Begin Part XII.
Begin Part XIII.
Begin Part XIV.
Begin Part XV.
Finish the game.