All of the items are referencing the same 'isHidden' value, so when you change it for one it changes for all. I'd so something like this:
<ion-card *ngFor="#item of items">
<img src="https://placehold.it/500x300" [hidden]="item.hidden" />
<button (click)="item.hidden = !item.hidden">Hide img</button>
</ion-card>
I haven't tested that at all but it should be pretty close to the mark.