Invalid_request: No auth function available for given request

Do you mean you want to call /1/metadata/link from JavaScript? I just tried that out, and got it to work like this:

$.ajax({
    url: 'https://api.dropbox.com/1/metadata/link',
    type: 'POST',
    data: {'link': "https://www.dropbox.com/sh/748f94925f0gesq/AAAMSoRJyhJFfkupnAU0wXuva?dl=0"},
    headers: {
        "Authorization": "Basic <base64(APP_KEY:APP_SECRET)>"
     },
    success: function(data) {
        console.log(data);
    },
    error: function(data) {
        console.error(data);
    }
})

Be sure to replace the <base64(APP_KEY:APP_SECRET)> with your base64 encoded app key and secret, as covered here:

https://www.dropbox.com/developers/reference/auth-types#app

(The technique of putting the app key and secret in the URL doesn't seem to work in JavaScript.)

Also, note that API v1, such as this endpoint, is deprecated:

https://blogs.dropbox.com/developers/2016/06/api-v1-deprecated/

You should migrate to API v2:

https://www.dropbox.com/developers 

The equivalent endpoint in API v2 is /2/sharing/get_shared_link_metadata. That doesn't support app authentication though.

Using that in JavaScript would look like:

$.ajax({
    url: 'https://api.dropboxapi.com/2/sharing/get_shared_link_metadata',
    type: 'POST',
    processData: false,
    data: JSON.stringify({"url": "https://www.dropbox.com/sh/748f94925f0gesq/AAAMSoRJyhJFfkupnAU0wXuva?dl=0"}),
    contentType: 'application/json',
    headers: {
        "Authorization": "Bearer <ACCESS_TOKEN>"
    },
    success: function(data) {
        console.log(data);
    },
    error: function(data) {
        console.error(data);
    }
})