The final three onslaughts in the devil's attack are the temptation to turn stones into bread (vv. 3-4); the temptation to gain “the kingdoms of the world” (vv. 5-8); and the temptation to cast himself from the pinnacle of the temple (vv. 9-12). These have been described as the physical temptation; the political temptation; and the religious temptation. We might think of them as three storm waves crashing upon Jesus, attempting to tear him down.
As an aside, we might note, again, that the first three Gospels all agree in stating that Jesus was tempted after his baptism. Mark’s account is very brief (Mark 1:12-13) and does not specifically describe the final three temptations. Matthew’s account (Matthew 4:1-11) is like Luke’s in that it also describes these final three temptations. You may know that Matthew and Luke do not agree in the order in which they describe the temptations (Matthew’s is bread, pinnacle of the temple, kingdoms of the world). Is this a contraction? No. Both agree precisely in the three temptations.
As for the order, consider this: I might tell one person in a conversation before church that last Friday I tutored my children in Latin, I played tennis, and I did some work in my garden. Over lunch, I might tell another person I tutored my children in Latin, I worked in the garden, and I played tennis. The fact that my ordering of these events differed in the two tellings does not alter the fact that it is absolutely true that I did all three of those things last Friday. I think there is good reason to believe that Luke’s account captures the chronological order. But the main point here is that “apparent” contradictions in Scripture evaporate when given enough time, reasoning, and information.