Ratcatchers

Starting out
Items required: A cat and some cat supplies.

Talk with Gertrude. She will tell you to speak to Phingspet and Grimesquit. They can be found in Varrock Sewer. After speaking with them briefly, your cat will have to catch eight rats before they will speak to you more. To find out how many rats you've caught, you can speak to either of them and they will tell you.

Catch eight rats in Varrock Sewers by clicking the "interact-with" option on your cat—then, speak to them again to receive a rat pole, and they will send you to talk to Jimmy Dazzler in Ardougne.

Jimmy Dazzler
Items required: A cat (If you have a kitten, bring a bit of fish in case it gets hungry, it will take significantly longer to complete this part of the quest with a kitten.)

'''WARNING: Be prepared to switch multiple worlds and spend 45+ minutes on this part unless you get extremely lucky. The guards simply having their backs turned is not enough to keep you from being seen.'''

Jimmy Dazzler can round the house unnoticed, and you need to go there avoiding the guards who will think you are an intruder. Jimmy will give you directions to follow to the house. Read them, and you will be prompted to go to the house (it is not located on the world map—you are teleported there instantly). You will find yourself in front of the house, in the gardens.

To make your way inside the house, you will need to make sure you don't draw the guard's attention; running permanently is advised and having lots of patience will help greatly. Guards will not notice your cat. There are three "save points"; upon reaching these points, any guards who see you will send you back to these points, rather than the beginning. Keep your cat in your inventory until you get inside the mansion. If you have a kitten, feed it after each room the kitten catches rats in so you don't forget.

From the start, facing north, run west south of the hedges or west across the bridge, either works if timed correctly. When the moment is right, dash behind the bushes in the northwestern corner, then behind the hedge north of the mansion, and then climb the trellis at the back of the mansion to reach a save point.

On the balcony, move as close as possible to a potted flower on the west side. Go inside the bedroom to the west, which is to your right if you are facing south, to find a rat and use your cat to catch it. Pick up your cat until you get to the next room. 'If your cat gets stuck behind a wall/object while moving around or getting to a room, click on Worn Equipment, and then the "Call follower" button at the bottom (looks like a whistle). Your cat will then teleport to be right beside you. You can use this as many times as needed.'

Find your way into the opposite bedroom on the east side across the hall and wait. Be patient, and when the guard closest to the eastern room disappears from sight onto the balcony and the guard closest to the western room has his back turned walking away to the west, enter the big room to the southeast with two rats, and catch these with your cat. Alternatively, one can enter the bedroom to the east and then wait for the guards to meet on the balcony, then run to the room where the two rats are found (it is directly south of the eastern bedroom—it has no door).
 * Note: If you're having trouble with this part, try logging on to a different world, as sometimes the guard's patrols become out-of-sync, making this part very difficult to complete.

Catch the two rats in this room; then, proceed down the ladder and catch the two rats in this room.

Go through the door to the north and catch the rat in the kitchen.

Note: There may be one rat in the western bedroom to catch.

All the rats need to be caught in order to proceed. There are a total of six rats to be caught.

Once you catch all of the rats, teleport out of the mansion and return to Jimmy Dazzler. He will give you access to the Ardougne Rat Pits and tell you about the next person you have to find: Hooknosed Jack.

Hooknosed Jack
Items required: A cat and lots of fish for it (even if you're using a fully grown cat, both raw or cooked fish works), a catspeak amulet, four pieces of cheese, rat poison or the ingredients for it (a vial, red spiders' eggs, and a kwuarm), a bucket of milk, a marrentill and unicorn horn dust.

You can find Jack in southeastern Varrock (look for the minigame icon). He will tell you about the rat infestation in a warehouse nearby. You need rat poison, and he will make you some if you give him a vial, red spider eggs, and a kwuarm. Use the poison on four pieces of cheese to create poisoned cheese; then, go to the warehouse south of the pub. Go in and climb to the top. Use your poisoned cheese on the four rat holes to poison them. Then, go back to Hooknosed Jack.

He will tell you that his cat, Pox, ate some of the poisoned rats. Go to the Apothecary (the potion shop in west Varrock). He will ask for a marrentill herb, a crushed unicorn horn, and a bucket of milk to make a special cat antipoison. Then, give it to Hooknosed Jack to cure Pox. Hooknosed Jack will then tell you that there is still one rat left - the biggest and most evil. Go back to the warehouse. Climb upstairs and inside a room, you'll see the King Rat, but you won't be able to reach it yourself. Pick up your cat, and use it on the crack in the wall to challenge the King Rat.
 * Note: Eight or more fish should be enough even for a kitten. A kitten has 4 Hitpoints while a hellcat has 6 HP (5-6 fish is enough for Hellcat), so bring food accordingly - the king rat has a max hit of 1.

Use fish on the crack in the wall (NOT CAT) whenever your cat takes too much damage, as it will die if it loses all of its Hitpoints. If you are low on fish, you can go down the ladder and log out then log back in to get your cat back. After you defeat the king rat, go back to Hooknosed Jack. He'll give you access to Varrock's Rat Pits and tell you about Smokin' Joe.

Smokin' Joe
Items required: A cat, a catspeak amulet, a pot, some weeds and a tinderbox. Go to Keldagrim via the entrance northwest of the Grand Exchange, the mine carts, the Blast Furnace minigame teleport, or the city's entrance east of Rellekka and talk to Smokin' Joe east of the mining shop (far to the east of east Keldagrim). He will tell you about a nearby rat problem. The only way to get the rats out is to smoke them out, but Smokin' Joe can't do it because of the poor condition of his lungs. Offer to help him. Use your weeds on your pot, then light it with your tinderbox and use it on the rat hole to the east of him with your cat out. Rats will come out the other side and quickly go back in. Wear your amulet of catspeak, then use your smouldering pot on the rat hole again, and your cat will offer to help. Accept, and your cat will ambush the rats and kill them. Talk to Smokin' Joe again, and he will give you access to Keldagrim's Rat Pits and tell you about The Face.
 * Note: If your cat disappears when you use the smouldering pot on the rat hole, simply log out and back in again, and it will re-appear next to you.

The Face and Felkrash
Items required: A cat, a catspeak amulet, a snake charm, 301+ coins (or 151 with a ring of charos (a)), a ring of dueling (for easier access to Pollnivneach).

You can find The Face in Port Sarim next to the fishing shop. She will tell you to talk to Felkrash in the rat pits. Go down the manhole and find Felkrash. She will tell you to get rid of all of Port Sarim's vermin at once.

Talk to The Face again. She will tell you about a snake charmer in Pollnivneach.  Warning:  If you do not speak to The Face before heading to Pollnivneach, the Snake Charmer will not discuss alternate methods of animal charming.

Go to Pollnivneach in the desert south of Al Kharid, past the Shantay Pass. To save time, you can take a carpet ride directly there for 200 coins (or 100 coins with Ring of charos (a)). You will find Ali the Snake Charmer south of the bar. Use one coin on his money pot to get his attention. Ask him about charming other animals, and he will go on to tell you that he and Felkrash had fallen out because of Felkrash's killing of animals. He says he will give you directions to kill the rats for one more coin than you have. Tell him you don't care about his offer and walk away slowly until you get the option to stop. He will reluctantly give you a music scroll and snake charm for 100 coins. You can charm him with the ring of charos to lower his price to 50 coins.
 * Note: If you already received a snake charm in The Feud, you will not receive another

Back in Port Sarim, stand outside the manhole where The Face is. Read the music scroll to find out that it contains eight notes. You might want to take a screenshot to help you. Click on your snake charm to open up the notes input. Select the proper note (follow the scroll's order), and use the higher octave button (located on the top left) only if it appeared above a note in the scroll. Once you select a note, you can navigate through the pages (one note per page) with the arrows on the top right. Repeat this for all notes. Once you're done, click "PLAY".

Your character will proceed to play the song, which will charm the rats. You'll see a cutscene where you lead the rats into the ocean just like in The Pied Piper. Talk to Felkrash to finish the quest.

Reward

 * Quest points
 * Thieving experience
 * A rat pole
 * The ability to train overgrown cats into wily and lazy cats.
 * The ability to name your cat (up to six letters long).
 * Access to the Rat Pits.
 * The ability to use the Minigame Teleport to the rat pits in Port Sarim, Ardougne, Varrock, and Keldagrim.

Trivia

 * Just before your cat kills the smoked out mice in Keldagrim, it will say "Exterminate! Exterminate!", which is a reference to the Daleks in Doctor Who.
 * Some guards in the garden will say I miss Billy and Bob *sigh*. This is a reference to the guards killed during the cutscene of the Garden of Tranquillity quest, where you were stealing the statue of the king. It doesn't matter if you have started the quest or not.