Alma the Younger only used the word tribulation a few times, but he used it to great poetic effect.
'Tribulation' is first used in the Book of Mormon by Lehi, as he blesses Jacob in 2 Ne 2:1 and then by Jacob himself in Jacob 7:26. Lehi and Jacob use the term to describe the (mainly) physical struggles of their exodus.
It's then left unused until Alma the Elder uses it in a short sermon to his people in the land Helam (Mosiah 23:10). Alma the Younger uses it twice during his penitential speech in Mosiah 27:28,32. In Alma 8:14 it's used to describe Alma's state of mind (this could be Mormon's voice or he could be quoting Alma, it's hard to tell). Alma the Elder and Alma the Younger both use the term in a different sense than Lehi and Jacob -- that of an inner, mental struggle against sin and wickedness. In the case of Alma 8:14, the sorrow of seeing those for whom you have stewardship enmeshed in the snare of sin.
It's used again in Alma 15:3 and Alma 15:18 to describe Zeezrom. Again, it's difficult to tell whether this is Mormon's voice or Alma's. This usage follows the convention of using tribulation to describe the inner struggle against wickedness that accompanies repentance.
The Ammonites see the Nephites suffering 'many afflictions and tribulations' on their behalf (Alma 53:13), this may be Mormon writing on his own, or he may be quoting Helamen (the son of Alma the Younger). Helaman uses the term twice in a letter to Captain Moroni 56:2 and 7 (the second use is obviously connected to Alma 53:12). All of these verses use tribulation more in the sense of a physical struggle than the struggle of repentance.
Captain Moroni uses the word in his epistle to Pahoran (Alma 60:26). His use shares the same connotation that Helaman's and the use in Alma 53:12.