Items required: A pestle and mortar, a raw cod, a knife, and bread.
Inspect Pirate Pete. Talk to the Cook in the next room. He will tell you to get ground cod, breadcrumbs, ground crab meat, and ground kelp. He will tell you that Murphy in Port Khazard will help you get the crab meat and kelp. Make sure to ask him each available question pertaining to the ingredients, or you may not be able to make them.
Note: It's recommended that you get extra kelp and crab meat, especially if you have a low Cooking level, as if you burn the fishcake, you will have to go back to do it all over again. Luckily, you don't need any more bronze wire and hides, so just get extra cod, bread, kelp, and the meat.
Under the sea
Items required: A pestle and mortar, A fishbowl (empty), a needle, 3 bronze wires, weight less than 27 kg, at least 5 free inventory spaces, and a weapon (optional but recommended).
Go to Murphy, who can be found at Port Khazard (Minigame Teleport to the Fishing Trawler), to get your fishbowl made into a diving apparatus. Put it on, then ask to go diving. Your weight must be under 27 kilograms. Have multiple empty inventory spots, as you will not be able to drop items underwater if you need to pick up new items. The nearby Bank chest may be useful. You may not bring a Cat with you, on the ground or in your inventory, and attempting to will prompt some amusing dialogue from Murphy. Once you're underwater, find a tall plant, and pick it for the kelp. Then, look for a crab pen to the north. Talk to Nung. He will tell you to get him five mudskipper hides.
Underwater, talking to Nung.
Head to the entrance to the mudskippers' cave, on the western wall of the underwater area. Pick up five rocks near the entrance to the cave and then enter the cave. While in the cave (and the crab pen thereafter), you will be able to wield weapons as normal as you will be standing upright. Kill five mudskippers (level 30 and 31) to get hides. (Remember to give them to Nung before surfacing, as they will disappear!) Take them back to Nung. Give him your needle and three bronze wire; he will let you into the crab pen after this.
In the pen, kill a crab and collect its meat. Grind the crabmeat and kelp you obtained.
Go back to the Cook. Use the ingredients on each other, and cook it to get a fishcake. Right-click and use it on (don't eat it!) Pirate Pete in the dining room for your reward.