Beating the Elite Four and becoming the next Pokemon champion has never been the only goal of Pokemon games - you'll also want to catch all the Pokemon that fill your Pokedex, and Shining Diamond and Shining Pearl are no different. You can normally find Pokemon all over the world or by trading version-exclusive Pokemon. However, some Pokemon require special methods to evolve or items to evolve. Togekiss is a great example, but luckily evolving your Togetic won't be too difficult.
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Your first step in evolving your Togetic is, of course, having a Togepi. However, unlike most Pokemon, Togepi can be a little painful to acquire, so you'll need to jump through a few hoops to get your hands on one. Togepi's evolution into Togetic requires maximizing her happiness, so it may take some time. Once you have your Togetic, the evolution process is simple.
All you need to do to evolve Togetic into Togekiss is to use a special evolution stone. Togekiss requires the use of a Polished Stone. There are several ways to find Shiny Stones, such as using a Pokemon with the Pickup ability. When you have your Polished Stone, you just have to go into your bag and use it on your Togetic. You now have a Togekiss and are one step closer to compiling your Pokedex.