The Icecrown Gunship Battle is a mandatory boss encounter if you want to reach The Lich King and get a shot at getting his mount Invincible, and a lot of players have reported issues with soloing this encounter. Fortunately it's very easy if you know how to do it once you know how to prepare.
What most people do wrong is that they forget to equip the Goblin Rocket Pack. This is an item that goes in your shirt slot, and you get it by talking to an NPC called Zaphod. Just remember to not only get it, but also to equip it before beginning combat, since you will be unable to equip it once combat has begun.
Once the Goblin Rocket Pack is on, begin the encounter and head towards a cannon. Aim this at the enemy ship and shoot a few shots to lower the health. At one point the enemy will freeze your ship, and now it's time to use the Rocket Pack to transport onto the other ship. Once there kill the mage that has frozen your ship, then head back to your own ship to finish the encounter.
When you win the loot will spawn in a big chest on your own ship.