Another new app this month is Hiragana Quest, which aims to teach you hiragana by breaking each character down into smaller building blocks and mnemonics. It's designed for complete beginners of Japanese to learn the writing system, so anyone can pick it up.
Each lesson presents a hiragana character, its romaji, and some audio. Then, there is a pronunciation keyword to help you remember how the word should sound when you say it. Then comes the story, tying in how the character looks (sometimes based off of its parts) with that pronunciation keyword.
Once you've memorized the story as best you can, it's time to learn how to draw the character. First you trace the character, following the strokes, as an animated diagram. Then you have to repeat it more, from memory.
As you progress, shapes that appear in more than one hiragana character will be taught as building blocks, which you can use to make learning the rest easier.
You can test yourself on your hiragana knowledge in the app as well. It shows you the romaji and lets you attempt to draw the correct character. If you aren't sure, you can choose to look at the hints: the keyword, building blocks, or the entire story, to see if you can remember how to write it. You can also grade yourself, and mark it as "give up" or "pass" to move on.
If the method works for the first seven hiragana characters, you have the option to purchase the rest of the hiragana, or both hiragana and katakana. It's quite pricey for an app that just teaches kana, but if you haven't been able to get them down with traditional methods of rote memorization or other mnemonic methods, it may be worth trying out.