If it were a movie, they would have to learn from past failed attempts at video game movies and western animated shows based on Nintendo properties. Here's a mini-list on what I think they would need to do.
1. Use caution with you who you work with, know who they are and what they did. Subsequently, if you are that company or director, have someone from Nintendo be a creative consultant, someone to act as your bridge to Nintendo when ideas come up or are needed and what guidelines there are. (Some movie are ruined by people who don't care about the source material. Best example is 1998's GODZILLA, giving me a reason why I'll never watch a Roland Emmerich movie again)
2. Work with someone who knows this is a big deal and won't treat it like the "brain killing sex simulating" garbage "concerned" parents keep calling it. If it were me, I wouldn't care if it were Steven Spielberg or Christopher Nolan. If they don't know or care about Zelda, there is no way I'd work with them unless I gave them a little history lesson. And by little I mean a good 2-3 hours worth of game events, non-canon media, history behind the creation and influences.
3. This is in case they're not sure how to present it, or if it were in 1989, look at similar works in the same genre for some ideas. You want Ganon's minions to look imposing and not facepalming-ly dumb? Read some Lord of the Rings and learn about the orcs. (Also, avoid water parks and boxers with hearts. And don't ripoff Moonlighting if your show has a different premise, age group and cast of personalities than Moonlighting.) All in all, know the genre at what belongs in it. (Now for a shot at Uwe Boll, if it is a mystery, don't add ugly ALIEN knock offs and pointless backstory just to somehow justify car chases and sex scenes)
4. In my opinion, it should be an original story that unites elements from various games that work together. Otherwise, make it based on the original, but add things not present to make it a "bringing us full circle thing" such as the Master Sword, the Gorons, Gerudo, make Impa actually appear rather than exist solely in the manual. Basically know what exists and how it will work.
5. This is where it gets tricky. Characterization. People defend the cartoon's portrayal of Link by saying he was a blank slate and anyone's guess would be accurate since little to nothing was known about him. I have two problems with that. First: Just because it was the only non-gaming media depiction of him, not counting the manga unreleased in the states, that doesn't mean we should automatically accept it. Second: Just because Link doesn't have a voice or a biography as big as all three Lord of the Rings, doesn't mean he's a blank slate. ACTIONS define a character, and his actions show him to be a brave, determined boy who knows how to use weapons and magic and proved himself capable of taking on an entire kingdom taken over by monsters without once needing someone else to bail him out. Also, the manual does say he had a personality trait, one that clashes with only one certain depiction... well two if you count CDI, it said he has a burning sense of justice. Sure, it's vague, but that one little trait shows he doesn't want money, or a kiss, in return for his heroism. Basically, study the characters, let what they do during the game events to get an idea of what character they are. So, final lesson, know the characters and, if needed, use traits from similar characters (Let's say Simon from Gurren Lagann, Luke Skywalker from Star Wars and maybe a little Lion-O from 2011 ThunderCats for Link) just because the characters probably never spoke, doesn't mean you can give them any personality of your choice that clashes with what the game suggests.
I gotta do a little blog about what I just said one of these days.