Well, quite obviously, the biggest external conflict that Katniss faces is the grim battle for survival that she must endure in the arena of the Hunger Games. It is this conflict that dominates a significant section of the novel, as she must use all of her skill and ingenuity to defeat and kill the other contenders whilst they are trying to do exactly the same thing to her. However, another important external conflict that exists in the novel is the way that Katniss, through her attitude of defiance, comes into conflict with the Capitol. Note what Haymitch tells Katniss in Chapter 26:
Listen up. You're in trouble. Word is the Capitol's furious about you showing them up in the arena. The one thing they can't stand is being laughed at and they're the joke of Panem.
Thus we can see that even after she has won the games, Katniss still has to struggle for her life. In addition to these two examples of external conflict, one of the central internal conflicts running through the entire novel is the way that Katniss is unsure about her feelings for both Peeta and Gael. The situation is complicated by the way in which she is forced to pretend to have romantic feelings for Peeta when she is not sure that she has them in the first place.
Katniss struggles against the Capitol, obviously, throughout the novel. This is the most notable of the conflicts. She is constantly fighting against the Capitol. She sneaks under fences to poach animals from the woods in the early chapters in spite of the possible consequences of caught. she does this because of the difficult circumstances placed o herself and her family by the Capitol.
Throughout the Hunger Games Katniss is fighting against the Capitoal and doing anythign she can to make everything difficult for them.
Katniss also has external conflicts with the other competitors in the Hunger Games. She must kill them before they kill her. To go along with this external conflict is the internal conflict of her feelings regarding murdering these other competitors. She knows that killing is wrong and under normal circumstances she would never commit murder. However, she is put into this situation not of her own free will and has no choice. The internal conflict comes from her own morality conflicting with her circumstances.
Katniss faces an external conflict trying to battle off everyone in the arena to win the hunger Games. She also has an external conflict when she fights with haymitch on how to get help and when they disagree.
She has an internal conflict with her feelings about peeta and gale.she also has an internal conflict with the decision she made when she chose to enter the hunger games
Some external conflicts that Katniss has is that she gets a lot of injuries during the hunger games. Internal conflicts she has is she doesn't know who to chose between Gale or Peeta. Gale was her childhood friend and he is still her best friend and Peeta and her kissed during the hunger games and Peeta likes her
One of the biggest external conflict Katniss has to deal with is how to survive and all she has to deal with to ensure survival within the arena. Because of this she uses her arches, skills, and smartness to her benefit all the while every single other competitor is out to get her as well. She also defies the Capitol and basically spits in its face and that is another conflict. As for internal, it could be the competing affections of Peeta and Gale and to ensure her family's safety as well as how she has been affected after the Hunger Games. She is unsure of who she loves at first and is more attracted to Gale but is torn between Peeta and her childhood love. AT the time President Snow is keeping a heavy watch on her as well and she can't risk her families safety and must comply.