Legal question, not Game Design. Moving to Business and Law.
Read FAQ 61: http://www.sloperama.com/advice/faq61.htm
And many other threads in Business/Law have asked similar questions - can be informative to read.

Here: I went back ten pages and found these topics. Not saying they're all spot on to your question but you will likely find many of them apropos.

http://www.gamedev.net/topic/659552-fan-made-games-best-ways-to-get-aprooval/
http://www.gamedev.net/topic/656692-asking-permission-to-use-someones-picture/
http://www.gamedev.net/topic/653671-may-i-use-warcraft3-modelstexturesetc-in-my-androidios-game/
http://www.gamedev.net/topic/650218-is-it-legal-to-take-a-picture-of-a-toy-to-use-in-game/
http://www.gamedev.net/topic/648238-could-i-publish-super-mario-bros-nes-clone-to-google-play/
http://www.gamedev.net/topic/647520-is-the-blue-danube-waltz-by-johann-strauss-ii-public-domain-yet/
http://www.gamedev.net/topic/647337-guns-in-games-copywright-issues/
http://www.gamedev.net/topic/646576-copyrighted-music-in-non-commercial-games/
http://www.gamedev.net/topic/645109-ok-to-steal-someones-idea-if-they-are-doing-a-crap-job-of-it/
http://www.gamedev.net/topic/645127-introducing-characters-from-other-games/
http://www.gamedev.net/topic/644751-using-images-of-famous-people-in-games/
http://www.gamedev.net/topic/643680-how-much-should-we-expect-to-pay-for-licensed-vehicles/
http://www.gamedev.net/topic/642543-the-legality-behind-games-that-make-obvious-references-to-another/

But to state it briefly: if the title is not used, if the IP's characters and place names are not used, if the original game's graphics and text and sounds are not used, then the IP has not provably been violated. Gameplay can't be copyrighted or trademarked, or probably even patented.

I'll add that, you can think of the process as coming up with an original animeish story and cast of characters of the same basic type as one or more existing animes. There are already many animes about ninja students, magic students, dragon riders, battle-doll controllers, and people for whom collectible cards/miniatures/dice come to life; as long as there are 2 existing examples it's a legal safe space for more.