Because it's an array and you're looking for an embedded property, not just a simple array value, there isn't really a super-efficient way to find it. There's the brute force mechanism of just walking through the array and compare each id to what you're looking for.
If you're going to be looking up these kinds of things in this same data structure multiple times and you want to speed it up, then you can convert the existing data structure into a different data structure that's more efficient for accessing by ID like this:
var imagesById = {
"1234": {"url":"asdf","tags":["cookie","chocolate"]},
"5678": {"url":"qwer","tags":["pie","pumpkin"]}
}
Then, finding an object by id is as simple as this:
imagesById["1234"]