The first was technically for his campaign in Africa vs the Numidians in support of Hiempsal II, but everybody knew that it actually included his defeat of Romans in Sicily (Carbo) and North Africa (Domitius Ahenobarbus) who were Marian holdouts. His first triumph was extra-legal, given that he was much too young and was elected to no office, but it happened anyway, to the annoyance of Sulla.
His second triumph was for his victories in Hispania vs the rebel Sertorius. Technically, the armies of Sertorius were of Hispanian origin, so it counted as a foreign enemy.
The third was over his campaigns in the east, which included a laundry list of defeated foes: Kingdom of Pontus, Armenia, Cappadocia, Paphlagonia, Media, Colchis, Caucasian Iberia, Caucasian Albania, Syria, Cilicia, Mesopotamia, Phoenicia, Judaea and Nabataea. It was held in 61 BCE and was by far the most indulgent and magnificent spectacle ever put on in Rome up to that point (and maybe thereafter, arguably).