Zelda is quite the punishing kind of character: She has low mobility and her best moves are her smashes. For that reason, she’ll mostly prefer to bait Ike once in a while with Din’s Fire and punish him really hard whenever he manages to lag near her. Winning as Ike is, mostly, pretty straightforward: He must just avoid doing that. In other words, don’t spot dodge inadvertently, space himself with aerials (watching out for her long ranged Fsmash) and always jab when close to her (her grab is quite short ranged, and getting shield grabbed is much less punishing than, as an example, getting hit by her Dtilt).
As for recoveries, Zelda’s can be quite as fragile as ours (though Ike is a much heavier character in comparison): Her teleport can travel in 16 different angles (though only 3 should be useful at a given moment), but boosts tremendous amounts of pre and post lag. It is not uncommon hitting Zelda out of it just after she disappeared. Ike could also punish her after she reappears by holding the ledge and performing a ledgehopped Fair when she appears on-stage consistently, if she is recovering from far enough (and vice-versa). Also, both are very menacing ledgeguarding each other, as in Zelda using Din’s Fire to explode Ike out of Aether and Ike using Nair to cover most, if not all, of Zelda’s recovery options during its execution. At close range, the Ike player should be wary she could reappear at a variety of positions, even right over him, damaging and pushing him away. For that reason, I would recommend to the Ike player to cover the trajectory that is closest to the center of the stage (which is preferable for the Zelda player).
As in all combat taking place with both characters on-stage Zelda requires that the Ike player fail to space himself correctly in order to triumph, and the jab still maintains itself as a formidable response at boxing range, I consider this matchup advantageous to Ike, as in a 65:35 advantage.