How to make eyes pop in outdoor photography?

I have a Nikon D3100 and I just taking pictures for family so I'm a beginner. I have a sister who has extremely light blue eyes, and she is light sensitive. She wants outdoor pictures during the day, and when I have done pictures for her in the past, the pictures result with her eyes as dark slits and you can't even see the beautiful color of her eyes. When i have used flash in the past it just gives them red eye or makes their skin look pasty and it darkens out the background. With it being a very sunny day, how do I get great detailed pictures with clarity in the eyes?

Have her stand in the shade as close to the sun light as possible… The very edge of the shade and tell her to look happily surprised. Her eyes should show then.

You use off camera flash with a large modifier, like a softbox or umbrella.

The modifier allows you to make the light source bigger (and therefore softer), and the flash off camera allows you to give some direction to the light - if it's off axis you won't get redeye. It will also give a good catchlight in the eyes which will make them sparkle.

I suspect you are using harsh, on camera flash (ie the pop up flash).

The correct way to meter the scene is to meter for the background sky, drop the exposure by a stop or so and then light your subject to the required level.

Don't have her looking into the sun as she's bound to squint and close her eyes.

You won't bring out the blue in her eyes using strong direct light. Use soft lighting (light bouncing off something else before reaching her) and shoot very close.