I don't have too much experience with Zelda, but don't go for Dair - AT ALL - When shes juggling you. You're likely to get beat to the punch almost everytime, so just go for bombs and mind games. You can juggle her pretty good yourself. You have to worry about her d-smash and f-smash a bit, so I would use some retreating Zairs, as a PS could lead to a strong smack in the face or a kick in the balls, if you get what I mean. To my knowledge, you can camp her decently, as her NL is a bit flawed, but don't underestimate her option to use it.
When you're grounded, use your step dodge to avoid Dins fire at all times, its rather easy actually. She can try to fake you out by exploding it infront of you rather than on you directly, so watch out for that and you should be safe. Watch out for it off-stage even more so as well, considering that could **** over your chance at making it back or put you in a better postion for her to gimp/spike you. Don't let her stage-spike you when you're hanging by your clawshot, either >_>
As for being up-close, as long as shes defensive she can overwhelm you (but I wouldn't say its ****, either), so do that somewhat sparingly.
Shiek ***** you manly, so jump off quickly. If you wanna struggle, however, I would pretty much say the same as with Zelda minus the Dins, avoid close combat even more, needles are a pain, he/she can rack up damage and gimp you like its nothing, and you aren't juggled as hard as with Zelda (I guess thats quite a bit different, actually ^_^; and worse). Shiek can get through your camping and spam after a while (not easy easy, but he/she will somewhat quickly), so I would suggest a little bomb spam (don't over do it), and see if you can catch them off guard with a grab to get them TFO.
Thats my take on the match-up. I guess 60-40 Zelda and 30/35-60/65 Shiek is about right. What if its a Shiek-to-Zelda player, though?