There are a total of five Firefly pendants in The University chapter of The Last of Us. The chapter consists of the sections Go Big Horns where you will find four pendants and Science Building where you will find one.
If you missed our previous chapter, Tommy’s Dam, be sure to check it out and get yourself one step closer to 100% completion.
A short time after the beginning of the chapter. Ride your horse up a set of stairs and through some archways. Turn to the right and you will see a couple of trees. The pendant is hanging from the tree on the right side. Use a brick or bottle found on the ground to knock from the tree.
Just before you jump a small obstacle with your horse, you will see a large building beyond the obstacle which appears to have a clock built into it. Dismount your horse and head to the right. You will need to climb on to a dumpster and into an abandoned building. There is only one room. The pendant is located on a desk near the window.
After you enter the dormitory, head up the stairs and explore the second level. You will come to a point where you have to drop through a hole in the floor. Once you do you will be faced with multiple Clickers and a Bloater. Toss a bottle or a brick near the main concentration of Infected. Once they move to investigate the noise hit them with a Molotov Cocktail or two. Only the Bloater should be left at this point. You can avoid him but he is carrying the Firefly pendant so you must kill him. If you have the Flamethrower found earlier in the chapter use it to take him down. If you do not have the Flamethrower again use Molotov Cocktails and Nail Bombs. Once he drops you will find the pendant laying next to his body.
After the dormitory but before the Science Building portion of the chapter. While riding your horse with Ellie you will come to an open area with several white tents. Be sure to search them all for supplies. At the very left side of the area, past the white box truck you will find two tents together. The pendant is in the last tent sitting on a table near the back.
In the Science Building portion of the chapter. As you progress through the story you will come to a door that when opened will trigger a small cut scene with some monkeys fleeling. The pendant is in the back right corner of that room sitting on a shelf.