She said she climbed mount Everest alone.
Do you believe what she said is true?
She's just really drunk and making stuff up.
It's understandable that you question the legitimacy of her claims. You shouldn't take to heart things that people say when they are drinking.
Maybe she really did do it, how am I to know?
I think a claim such as this is one you can disregard. Climbing Everest alone seems near impossible. Wait until she is sober and then ask her again.