Although the purpose of the game is to defeat other Magikarp in various contests of jumping, the focal point of the game is in raising the Magikarp, and there are three different elements to the process.
Like all Pokémon games, you need to capture a Magikarp. The capture in this game starts off the same as all others. You get given a choice between three different rods, with the alternate colours unlocking after you have beaten the Mega League. Then, your character goes and fishes the Magikarp. There are many different styles of Magikarp, each with different rarities.
When the Magikarp is captured, it has a maximum level based on your current trainer level. It will also display the Jump Power Bonus you have at your current trainer level, and a special individual bonus that it has. These bonuses are random and have effects just for this Magikarp. It then stacks with other bonuses from decorations and the standard bonus. The value of the individual bonus is random
If, when you have caught a Magikarp you decide that it isn't what you want, then you can spend 10 Diamonds to fish again to try for another one, or 50 if that one isn't good.
Each Magikarp you catch has certain potential listed by the Fisherman:
Raising Magikarp is fairly simple. Basically, feed it Food in the aquarium, take it on Training Regimes, or even from some Events. This will give it increased Jump Power. As its Jump Power increase, it level increases. However, the maximum level it can be is only 10 higher than your trainer level at time of capture.
As Jump Power is gained, Magikarp will level up and when it reaches certain milestone levels, it will grow to be bigger, sometimes getting a new look and style in the process. The Magikarp's appearance will not register in the game's list until it has reached a higher level. At first, this happens at half of the Pokémon's maximum level, but as you get higher levelled, your Pokémon will grow multiple times. Every 5 levels you gain, a Poké Ball will appear with Coins as well.
In addition to this, you'll always have a bonus given by Mayor Karp, which is increased whenever you max out a Magikarp. This really aids in the speed you can level up your Magikarp.
While growing the Magikarp, you can take it to the leagues without fear of losing it when you lose, but when the Magikarp is at its strongest...
Unfortunately, the Magikarp you raise will not be with you forever. As it has a finite amount of Jump Power that can be gained, it only has so much use and so there are multiple times where you can lose the Magikarp. It's not just from reaching the top Jump Power amount that causes it to be lost, but rather a multitude of things
First, if you lose a league match with Magikarp when it's not at its top Jump Power, you won't have to worry as you won't lose Magikarp this way. If, however, you have Magikarp at the highest it can be and lose a match, then that Magikarp will return with you to the aquarium to retire and just be visible in the background.
In addition to this, there are a few high risk Events that could result in you losing the Magikarp. These events are optional and you can always decline them and get some Jump Power, but if you accept the event, then you have a chance of getting more Jump Power or you could lose the Magikarp through things such as a Voltorb exploding or a Pidgeotto carrying Magikarp away.
Finally, there's an option in the menu after you reach rank 15 to retire the current Magikarp and replace it with a new Magikarp, so you can do this if your Magikarp isn't the right one that you desire.
Once you have lost the Magikarp, Mayor Karp will give you some experience for your trainer to help you level up to the next level in order to get a stronger Magikarp and conquer the next stage.