Enemies
During the game, Rose pursued a variety of opponents with Dart and the other Dragoons. Some they were successful in stopping but others constantly got away and the group was forced to give chase. While many of the party members were motivated by a particular event or person, Rose was motivated by her overarcing mission and curosity. It wasn't until the the two overlaped that it became personal.
Emperor Doel
"All is ordered by the reborn Emperor Diaz. Lloyd is a mere pawn. Along with the Dragoons...."
Greham was the first to mention Doel's association with Diaz. At some point, Doel was given the Violet Dragon Spirit, the spirit granting him great power. While Doel's methods were bloody and violent, Doel truly believed that King Carlos was a poor ruler that would destroy Serdio. He believed that by killing Carlos and taking over the throne, Serdio would be a better place to live. However Doel also believed he could control Lloyd and the Dragoons. He likely had no knowledge of the utopia Lloyd was trying to create or Diaz's true motives.
Rose became interested in all the talk about a living Emperor Diaz and in turn, interested in Doel's role in it all. She likely felt no animosity towards the man as Rose had no concern over who sat on the Serdio throne. All she wanted from him was information about how he obtained Dragoon Spirits and where Diaz was. Unfortunately she never learned this information but gained a little knowledge of a conspiracy that would cover Endiness.
Lloyd
"I... just desire the power to create a utopia."
Throughout the game, Lloyd gave Dart and his companions very good reasons to hate him. He killed Lavtiz, kidnapped Queen Theresa, abandoned Lenus and caused trouble for everyone involved. With Rose, it was his pursuit of the Divine Moon Objects, possession of the Dragon Buster and mentioning of Holy Emperor Diaz. Having personal knowledge of the items and the man, she naturally wanted to know what the hell he was talking about. She would have obviously known he was a Wingly however that didn't matter. His actions were more important than his species.
Lavitz's death was horrible, but Rose had lost more important people in her life. She was not about to go and avenge anyone's death if it would interfere with her greater goals. Rose had the least amount of hate and anger toward Lloyd than any other party member, if any at all.
After Lloyd returned to fight against Melbu Frahma, it was Rose he gave the Dragon Buster to before his death. This gesture was odd in that the hero would usually receive the powerful weapon from their former adversary in that situation. Dart was recognized by the Divine Dragoon Spirit and one could argue that it was a gift however Lloyd really didn't have a say in who was recognized so he couldn't really give it as a gift.
Lloyd's gesture might have been kinship or perhaps he felt that Rose was the most deserving of the weapon. After learning of her role as the Black Monster, he might of felt guilty for undoing everything she had done to protect the world. Regardless, when Lloyd died, he and Rose were at an understanding and left no animosity behind.
In fanfiction, Rose and Lloyd are a very common pairing.
Lenus
"Surprised, huh? This is the true self of Miss Lenus!"
Lenus worked for Lloyd and helped mastermind the kidnapping and switch of Princess Emile with herself. For six months she did whatever she wanted in the palace, living a life of leisure while waiting for Emile's 21st birthday at which time she would be given the Divine Moon Dagger. It was supposed to be easy. Luckily for Tiberoa, Dart and his companions showed up and started to unravel the secret behind the Princess' sudden change of personality.
Rose had no open hostilities towards Lenus. For the most part, she didn't know that Princess Emile was a fake although she likely had suspicions something was amiss. Once Lenus revealed herself, Rose was quick to draw her sword and promise Lenus death for stealing the Divine Moon Dagger. Rose would have been the only person who knew the real purpose of those items and could deduce what Lloyd might be using them for. She was also aware that Lenus was also a Wingly. It wasn't personal, however Rose would not let anyone threaten the world's peace.
Divine Dragon
Rose was aware of the Divine Dragon's existence and quite aware it had been imprisoned since the Dragon Campaign. She knew it was a creature that couldn't be controlled by Dragoons let alone anything else. It was the epitome of a dragon. It was a beast of impossible power that did not have the intelligence to control it. The Divine Dragon was a threat to Endiness. It would continue a path of destruction against anyone it felt had wronged it.
Rose knew it had to be stopped but also knew that such a task would be impossible without the weapons that helped seal it in the first place. The first weapon was obviously in enemy hands. Lavitz had learned that. The second was the Dragon Block Staff and it so happened the little Wingly traveling with them knew where it was.
Rose fought the beast to protect all of Endiness. It had already destroyed a Signet Sphere. Rose would not allow it to threaten all her work protecting the world from the Moon Child only to have it open the way to the Moon That Never Sets.
Zieg
"My hands start the world, and my hands end the world. Yes! Fate desires it."
Rose chased Zieg to find out what happened to him. The Zieg she encountered in Vellweb was nothing like the Zieg of her past. How could a man that fought to free everyone from Wingly rule turn around and decide to destroy the world? He fought against fate only to enforce Soa's fate years later. Rose could not and would not accept this. Something was wrong.
Zieg was able to fly, to cast magic. Humans could not do these things. That was the whole purpose of Dragoons. Rose did not learn until the very end in the Moon That Never Sets that Melbu Frahma had gained control of Zieg when Rose attacked Neet as the Black Monster. It was moments before the final battle that Zieg and Rose were able to reunite.
Rose chased Zieg to protect their revolution even though he no longer appeared to care about it. While she had no desire to harm him, it is likely she would have tried to kill him if that's what it came down too. Even Zieg would not be spared if he desired the destruction of the world.
Melbu Frahma
"In order to obtain an eternal body that is proper for an immortal soul!! And now, I am becoming a god!!"
Rose carried a hatred of 11,000 years. Frahma was the man who enslaved her people, killed her friends and fiancée and caused her bitterness. Because of Frahma, Rose must kill children forever. Frahma doesn't think too highly of her either. Assisting in his downfall and everything.
At the end of the game, Rose discovered that Frahma had been controlling Zieg. Along with Dart and her new friends, she killed the newly born god only to have him rise again. This time, she and Zieg ensured he would not return and gave their friends a chance to escape with Shana. Frahma, Rose and Zieg no longer had a place in this world.