The Hydraxian Waterlords is the first raid reputation for WoW. You can increase your reputation with the Hydraxian Waterlords by killing mobs and bosses in Molten Core. The normal mobs in MC will give you reputation until the end of Honored. After you reach Revered the only way to gain reputation is by killing a boss. Depending on your class, gear and kill will determine if you're able to kill a boss.
Usually if you can heal in one way or another you'll be able to solo Lucifron and maybe Magmadar. Also, while you're plowing through molten core you'll want to save the Fiery Cores, Lava Cores and Core Leather, if you have skinning. These can be used to increase your reputation with the Thorium Brotherhood. The items you'll want to save are as follows
Dark Iron Ore (If you have mining)
Blood of the Mountain (If you have mining)
For tips and strategies on how to beat the bosses in Molten Core please follow this link.