(I imagine this happening right after a shipwreck where Anna and Elsa get separated. This is the start of Anna and Hiccups friendship. It could either only be a friendship or it could turn into something romantic. You can decide)

Washed ashore Anna lay knocked out in the sand next to a couple crates, broken pieces of rope, broken wood and a sword made of ice.
The princess stirred and lifted herself out of the sand. She was soaked to the bone.
"Where am I?" She wondered aloud.
The grey sky, hinting that rain was coming soon, made the beach almost eerie. Anna felt almost lucky to have washed up on sand instead of the sharp rocks that enveloped the cove. she shivered as she brushed of the wet sand from her cloak. The beach was almost surrounded by rocks and cliffs except for a part that lead into a forest. She shivered again. She was drenched in cold sea water and the chills of the damp fall air didn't help.
"I need warmth" she thought. She grabbed some of the broken wood, some of the rope and packed it into an empty crate. The longest piece of rope was used to craft a makeshift belt to hold the sword. Then she headed to the forest. To hopefully find a cave for shelter.
Anna soon found a cave with a hot spring towards the back of it. She cleaned her clothes up and dried off. She needed a fire and soon. She grabbed the sword and went off to go find some fire wood. She would have to get enough to last her the night.
Elsa's magic ice sword didn't show any signs of melting. Elsa and Anna were having a competition between the two of them before the storm hit. Anna was thrown from the ship.
"I got to look for them first thing tomorrow... or at least a way off this island" she muttered to herself.
The forest was deathly quiet. Anna kept on her toes. And although the sword was handy she would've preferred an ax at this point. She had gathered a good amount of firewood made multiple trips and headed back to the cave.
It was dark by the time she actually got a fire going. For it being fall the cave was really warm. Must be because of the hot springs. Anna thought. Even the floor of the cave was warm enough to rest on. She fell asleep.

     She awoke to this blazing heat and chittering. She shot up thinking that she rolled to close to the fire. But the fire was out. The chittering grew louder. The heat became more intense. Anna was sweating like crazy. The walls and floors began to move. Then glow. Lizard like creatures covered every inch of the cave. Anna backed away as slowly as she could. An ungodly screech-like roar came from the back of the cave. The lizards started attacking. Anna grabbed her sword, her bag, and ran. She sprinted out of the cave. The small lizards were now on fire setting the grass and trees around them on fire too.
Through the forest Anna ducked behind trees and shrubs. Again came the roar. Anna looked over her shoulder. Something big was coming, it tore down trees with it.
She came to a small clearing. She paused. Out in the open was a dangerous play. She could feel the heat on her back. She didn't have a choice. But it was too late. A gigantic glowing reptile landed in front of her and stood in her way. A roaring flame at her back and a dinosaur in front of her. Anna was trapped. She held her sword high. She wasn't about to give in without a fight.
The reptile was yellow, red eyes. A crown of scales and lots of legs. And although it was on fire, Anna's ice sword was not melting. The reptile reared and hissed.
Splash. Anna and the reptile were soaked A strange green reptile with a large stomach was spraying the forest with water.
Suddenly a person appeared with a mask and a flaming sword. The reptile stared hissed and retreated back from whence it came. Anna watched in amazement as the creature roared and went back into its cave.
"Don't you know any better than to enter a dragon's nest. Especially a fireworm nest?" A mans voice came from the figure with the flaming sword. Anna still with her ice one raised.
"I thought dragons were only myths from story books." Anna said fiercely not letting her guard down. He may have saved her but she wasn't about to take chances.
"And yet even in a fireworm nest you're sword didn't melt." He retorted.
"It was made by my sister, She has... Ice... magic." Anna let her sword drop. Ice magic at this point did seem more ridiculous than dragons.
"Ice magic?" He questioned.
"Yes ice magic. It came from the queen of Arendelle." Anna stated proudly. Stories of Elsa had been spread all across the lands. Most of them bad some the truth.
"Ah yes the stories of the merciless Queen who froze her kingdom and tried to kill her sister.... which I'm assuming is you." He was calm.
A black blur came bounding up to this man.
"Hey bud easy stay behind me." He ordered the beast. Another dragon black as night and striking green eyes stared at Anna and her sword. Its eyes turned to slits as it waited behind it's master.
"Who are you?" Anna asked.
The man removed his mask to reveal shaggy brown hair and forest green eyes. He had small amounts of stubble on his chin and a small scratch on his chin too.
"My name is Hiccup. Chief of Berk. A safe haven for dragons." He stated proudly. Still holding his flaming sword.
Berk sounded familiar. Maybe from an old geography lesson. A peaceful country if memory served correct. Anna new that she was not gonna find home without his help. She sheathed her sword.
"My name is princess Anna of Arendelle. I was thrown from my ship and I washed up on your shore. I need help getting back home. Will you help me?"