Why does she have issues?
The media and magazines and judgy popular kids at school and work constantly poke and prod at minor aspects of women, helping them feel unattractive. They point at minor aspects of women like jiggly bellies, saggy underarms, skin damage, and lots of things like that. I don't know what your friend specifically is up to, but it's a recurring issue that women feel bad about themselves because of the media and popular kids.
This is a powerful and regular flow of negativity towards them, making it hard for them to change their minds, telling them that they look bad, that they're acting wrong, that everything about them is inferior. This stuff is all telling them that to get a good job or a good partner they need to look better. It doesn't matter how smart they are or how good their personality is, what matters is how they look.
Of course, they can never meet these standards. They're comparing themselves to the beauty of women with teams of photo editors, makeup artists and expert wardrobe people with a limitless budget. Rationally, they can't compete.
Even if they do reach these heights, they won't feel secure. They had to put in massive effort to reach these levels of beauty, so they're not naturally this beautiful, or fun. Their breasts don't bounce perfectly without a bra, their face doesn't look smooth and makeup covered when they wake up. There's enough media pictures of women bounding out of bed with perfect makeup and hair, why can't they?
There may also be specific issues with her that make her insecure. Maybe she's not a girly girl and feels she needs to be more feminine to be attractive. Maybe she was fat in the past, and feels insecure about it. Maybe she was heavily bullied and still remembers those words today. Be aware of those potential flash points.
How do you not fix this?
Saying stuff like "no, you're wrong, you're very beautiful/no one finds you annoying"
Let's break it down. First, you're denying all the media things, popular kid comments, and negative experiences she has had. Lots of people probably do find her unattractive or annoying, because there's a whole industry out there fueling this. They make money off of women feeling bad about their bodies and personalities and buying expensive products to fix it, and they're very good at poking at insecurities.
Second, there's a good chance she feels you're just saying that as an obligation to be nice because she's your girlfriend, or to shut up because her complaining is annoying.
Third, she's saying she feels ugly or annoying. That's an emotional issue. You can't argue people out of their emotions.
How to fix this?
There are several ways to help. One way is regular compliments. They should be specific, and not "You're gorgeous" And more like "I love your hair, it's so stylish." or rub your girlfriend's arm. "You look so fit today." or "Haha, I love spending time with you, you're so funny." These specific compliments look less like a lazy obligation compliment and can help boost self esteem.
If she rejects the compliments, just say "I meant what I said" And move on. I personally found in relationships that this generally raised the self esteem of my girlfriend, and I got more and more smiled and relaxed behaviour.
Be aware of what she values in terms of compliments. Some women only believe PDAs in terms of proving affection, some like gifts, some like compliments. PDAs are of course not generally appropriate for non girlfriend friends.
Don't judge her for minor stuff. Be careful with stuff like saying "You look tired" or "You look sad" or other stuff that will look like a subtle attempt to say they're ugly or annoying. I've popped pimples, dug splinters out of feet, and done lots of weird things with girlfriends without judgement as well. Avoid judgement.
Also, talk to them and listen. Ask them why they feel like it. There's often ways to help out if you know specifically why they feel that way. Maybe they feel like they can't compare to Kim Kardassian, but haven't seen her pictures without makeup and Photoshop. Maybe they are having a fight with a friend. Maybe someone bullied them and they want to talk.