How to create an attachment using WebApi in Dynamics 365

createActivityAttachment.js

var activityId = "059C0532-906C-E711-9409-00155D018D00";
var activityType = "appointment"; //or any other entity type

var entity = {};
entity["objectid_activitypointer@odata.bind"] = "/activitypointers(" + activityId  + ")";
entity.body = "ZGZnZA=="; //your file encoded with Base64
entity.filename = "test";
entity.subject = "test";
entity.objecttypecode = activityType; 

var req = new XMLHttpRequest();
req.open("POST", Xrm.Page.context.getClientUrl() + "/api/data/v8.2/activitymimeattachments", true);
req.setRequestHeader("OData-MaxVersion", "4.0");
req.setRequestHeader("OData-Version", "4.0");
req.setRequestHeader("Accept", "application/json");
req.setRequestHeader("Content-Type", "application/json; charset=utf-8");
req.onreadystatechange = function() {
    if (this.readyState === 4) {
        req.onreadystatechange = null;
        if (this.status === 204) {
            var uri = this.getResponseHeader("OData-EntityId");
            var regExp = /\(([^)]+)\)/;
            var matches = regExp.exec(uri);
            var newEntityId = matches[1];
        } else {
            Xrm.Utility.alertDialog(this.statusText);
        }
    }
};
req.send(JSON.stringify(entity));