For the Lesser Dog, pet him until you may have a tiny problem. Then spare him. To defeat the largest dog, the Greater Dog, you must play with him, then pet him, and continue playing, then pet him some more. To defeat the Dogamy and Dogaressa combo, roll in the dirt or snow. Then pet them. You should be able to spare them.
You should be able to buy things from the shop at the town nearby, called Snowdin, and raise your health from the inn. If you feel that you are ready. It's time for the second boss fight. Continue going right across Snowdin, and you will find Papyrus. After his monologue, you will enter the boss fight. His Blue Attack is like Doggo's. If you don't move, the blue bones will not hurt you. And, when he turns your soul blue, you have to jump. You must progress the dialogue to defeat him. You have to Act or Spare him. If he gets your health down to one, he will capture you. Don't worry, you can just get more items from the shop and try again. When you eventually beat him, you can be his friend. Then you can come to his house and look around. It's time well spent, because you can get his phone number and ask for help. You may enter a date, where you and Papyrus must try to outdo each other in manners and presents, that Papyrus hides in his hat.
When you "win" the date, you should keep going past Snowdin. You will enter the next area of the game, Waterfall. You'll meet Sans, at one of his jobs. He will take you to his favorite restaurant, Grillby's. You can order fries or a burger, but Sans will just have his favorite food... ketchup. After "eating", you can go back to Waterfall and trek onward. You will see a waterfall, and if you go behind the waterfall, you will find a hidden room. Soon, you will see Papyrus reporting to the Captain of the Royal Guard, Undyne. He will attempt to defend your case, but he will be sent back out to Snowdin. Then, the mysterious Captain will be alerted to your presence. You will be allowed to pass, and you will continue your journey. You will find the Monster Kid, who is a big fan of Undyne. When you progress to the right, you will find the Bridge Seed rooms. The solutions are not very easy, but you must stay determined.
After solving the puzzle, Papyrus will call to ask what you are wearing. You should change armor after that. Soon afterwards, you should see a wishing room, full of flowers. In that room, you can learn a little history. You should leave to the north, and you can step on a raft that takes you to the next room. Be on your guard, because Undyne will attack shortly. You have to run from her spears while going right. If a spear touches you, you will go through a short fight sequence where spears rain down from the sky.
Once you escape that room, you can save your progress again. In the next room, you will encounter Sans, who has a very... special telescope. Progressing forward, you will find a room where the colors are reversed. It is a small maze, but it is fairly easy to solve. Continuing forward, you will discover a strange and lonely creature, Onionsan. She is a large sea creature that looks like an onion. The next room has a monster called Shyren, a statue, and a piano. You have to play the melody by pressing Neutral [•], Up [↑], Right [→], Neutral [•], Down [↓], (Neutral [•],) Down [↓], and Right [→]. Once you leave that area, you will find an artifact. You're carrying too many dogs?!
Leaving that room and heading to the right of the statue will take you to a room where it is raining. Take an umbrella. Monster Kid will come and walk alongside you for this room.
After that area, you will enter another spear area. Where the ground turns blue, a spear will come. Avoid the spears while going right again. Look at Undyne, and you should take the route that she takes. You can escape her, and she will destroy the bridge you are on. You will then fall into a garbage dump. Go left and then north. A dummy will come to life, it will attack you. The way you must defeat it is by making its dummies shoot at him instead. Then Napstablook, the depressed ghost, will come along, and you can visit his house. Next, there will be mazes that get darker and darker.. and if you go to the bottom right corner, there is a surprise if you walk off the trail and down...
Temmie Village! The strangest area in the game. If you still have your Dog Residues, you can multiply them and sell them to Temmie and get infinite gold. Also,if you send Temmie to college, she will sell a very special item.
After all the mazes and puzzles, you will find a bridge. Undyne will appear, and so will Monster Kid. He will fall off the bridge, and you must save him. After He defends you, Undyne and the Monster kid will leave. In the room above you, you will meet Undyne herself. You must battle her. In her fight, spears will fly from all directions. Block the spears by pressing the button on your arrow pad that point to the spear in question. When you get the chance to, flee towards the cave behind her. Put up a chase until you reach the next area.