[Xposed Framework Modules] Riekr:
request from the click in the op's example:

GET /redirect.php?app_id=5&fid=3793&url=http%3A%2F%2Fbit.ly%2F1gf00Wo HTTP/1.1
Host: pt.tapatalk.com
User-Agent: Mozilla/5.0 (Android; Mobile; rv:29.0) Gecko/29.0 Firefox/29.0
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-Language: it-IT,it;q=0.8,en-US;q=0.5,en;q=0.3
Accept-Encoding: gzip, deflate
Connection: keep-alive

response:

HTTP/1.1 302 Moved Temporarily
Server: nginx/1.4.7
Date: Tue, 20 May 2014 10:43:04 GMT
Content-Type: text/html
Connection: keep-alive
X-Powered-By: PHP/5.5.9-1~dotdeb.1
Location: http://link.tapatalk.com/api/click?key=a7e5ffb24b9e84f4f4f6bbd88aa4e5b8&out=http%3A%2F%2Fbit.ly%2F1gf00Wo&subId=c157297d1a1ff043255bfb18530caaa2
Content-Length: 0

last request gets opened in firefox so the intent will not go through standard android intent but here is the rest of the dialogue, request/response each:

GET /api/click?key=a7e5ffb24b9e84f4f4f6bbd88aa4e5b8&out=http%3A%2F%2Fbit.ly%2F1gf00Wo&subId=c157297d1a1ff043255bfb18530caaa2 HTTP/1.1
Host: link.tapatalk.com
User-Agent: Mozilla/5.0 (Android; Mobile; rv:29.0) Gecko/29.0 Firefox/29.0
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-Language: it-IT,it;q=0.8,en-US;q=0.5,en;q=0.3
Accept-Encoding: gzip, deflate
Connection: keep-alive

HTTP/1.1 200 OK
Content-Type: text/html
Content-Length: 5681
Connection: keep-alive
Date: Fri, 11 Apr 2014 03:56:13 GMT
Cache-Control: max-age=15, must-revalidate
Last-Modified: Mon, 22 Apr 2013 23:46:42 GMT
ETag: "a7ceedbb01d08d67261e38ef35e8325d"
Accept-Ranges: bytes
Server: AmazonS3
X-Cache: RefreshHit from cloudfront
Via: 1.1 09052d1a6e392e4f4a3fd97bf34a2b24.cloudfront.net (CloudFront)
X-Amz-Cf-Id: _HLoQ4TOmngisOGi_FvFoJaZTN0CQ9Wov1q5ZrgltEXI2ye1AbLUJQ==

<!doctype html>
<html lang="en">
<head>
<title> </title>
<style type="text/css">
h1 {
color: #888;
font-size: 25px;
margin: 0;
}
p {
margin: 1em 0 0;
}
#error {
background-color: #fff;
font-family: "Lucida Grande", sans-serif;
font-size: 13px;
padding: 60px;
position: absolute;
top: 0;
bottom: 0;
right: 0;
left: 0;
}
#error div {
background-color: #fff;
border: 1px solid #999;
padding: 1.7em 2em 1.9em;
border-radius: 8px;
margin: 0 auto;
width: 80%;
-moz-border-radius: 8px;
-webkit-border-radius: 8px;
}
</style>
</head>
<body>
<noscript>
<div id="error">
<div>
<h1>JavaScript Unavailable</h1>
<p>
We can't automatically redirect you because JavaScript isn't available.
<a href="http://api.viglink.com/api/referrer-redirect">Click here to continue</a>.
</p>
</div>
</div>
</noscript>

<script type="text/javascript">
( function() {
var

opts = {
api_url: "//api.viglink.com/api/click",
timeout: 2000
},

$ = {
createEl: function( name, attributes, css, doc ) {
var i, el = ( doc || document ).createElement( name );
attributes = attributes || {};
css = css || {};

for( i in attributes ) {
if( attributes[i] !== undefined ) {
el[i] = attributes[i];
}
}
$.css( el, css );

return el;
},

css: function( el, css ) {
var i;

for( i in css ) {
try {
el.style[i] = css[i];
} catch( e ) {}
}

return el;
},

err: function( title, msg ) {
var wrapper_el = document.getElementById( "error" ) || $.createEl( "div" ),
inner_el = $.createEl( "div" ),
title_el = $.createEl( "h1" ),
msg_el = $.createEl( "p" );

wrapper_el.innerHTML = "";
wrapper_el.id = "error";
wrapper_el.appendChild( inner_el );
title_el.appendChild( document.createTextNode( title ) );
inner_el.appendChild( title_el );

if( msg ) {
msg_el.appendChild( document.createTextNode( msg ) );
inner_el.appendChild( msg_el );
}

document.body.appendChild( wrapper_el );
},

jsonp: function( params, callback ) {
var api_url, callback_name, ref_el, script;

params.jsonp = "jsonp";
params.format = "jsonp";

window.jsonp = ( function() {
var called = false;

return function() {
if( ! called ) {
called = true;
callback.apply( null, arguments );
}
};
}() );

params = $.toQuery( params );
api_url = opts.api_url + ( params.length ? '?' : '' ) + params;

setTimeout( window.jsonp, opts.timeout );

script = document.createElement( "script");
script.type = "text/javascript";
script.src = api_url;
ref_el = document.getElementsByTagName( "script" )[0];
ref_el.parentNode.insertBefore( script, ref_el );
},

toHash: function( str ) {
var i, ii, k, v, parts, params = {}, pairs = str.split( "&" );
for( i = 0, ii = pairs.length; i < ii; i++ ) {
parts = pairs[i].split( "=" );
// chrome throws an exception if the url part is improperly encoded
try { k = decodeURIComponent( parts[0] ); } catch( e ) { k = null; }
try { v = decodeURIComponent( parts[1] ); } catch( e ) { v = null; }
if( k !== null && v !== null ) {
params[k] = v;
}
}
return params;
},

toQuery: function( obj ) {
var k, qs = '';
for( k in obj ) {
if( obj[k] !== null && obj[k] !== undefined ) {
qs += '&' + encodeURIComponent( k ) + '=' + encodeURIComponent( obj[k] );
}
}
return qs.substr( 1 );
}
},

x = {
onApiClick: function( original, result, copts ) {
var i,
url = result || original,
redirect = function() { location.replace( url ); };

if( typeof copts === "object" && ( copts.tracking || copts.image ) ) {
i = $.createEl( copts.tracking ? "iframe" : "img",
{ src: copts.tracking || copts.image },
{ height: 0, width: 0, visibility: "hidden" }
);
document.body.appendChild( i );
setTimeout( redirect, opts.timeout );
} else {
redirect();
}
},

onLoad: function( e ) {
var params = $.toHash( ( location.search || location.hash || "#" ).substr( 1 ) );

if( ! params || ! params.key || ! params.out ) {
if( params.out ) {
location.replace( params.out );
} else {
$.err( "Missing Data", "We can't send you to that link because required data is missing." );
}
return false;
}

document.title = params.out;

$.jsonp( params, function() {
var args = Array.prototype.slice.call( arguments );
args.unshift( params.out );
x.onApiClick.apply( x, args );
} );
}
};

window.onload = x.onLoad;
}() );
</script>
</body>
</html>

GET /api/click?key=a7e5ffb24b9e84f4f4f6bbd88aa4e5b8&out=http%3A%2F%2Fbit.ly%2F1gf00Wo&subId=c157297d1a1ff043255bfb18530caaa2&jsonp=jsonp&format=jsonp HTTP/1.1
Host: api.viglink.com
User-Agent: Mozilla/5.0 (Android; Mobile; rv:29.0) Gecko/29.0 Firefox/29.0
Accept: */*
Accept-Language: it-IT,it;q=0.8,en-US;q=0.5,en;q=0.3
Accept-Encoding: gzip, deflate
Referer: http://link.tapatalk.com/api/click?key=a7e5ffb24b9e84f4f4f6bbd88aa4e5b8&out=http%3A%2F%2Fbit.ly%2F1gf00Wo&subId=c157297d1a1ff043255bfb18530caaa2
Connection: keep-alive

HTTP/1.1 200 OK
Cache-Control: no-cache
Cache-Control: no-store
Content-Type: text/javascript;charset=UTF-8
Date: Tue, 20 May 2014 10:42:05 GMT
Expires: Thu, 01 Jan 1970 00:00:00 GMT
P3P: CP="ALL IND DSP COR CUR ADM TAIo PSDo OUR COM INT NAV PUR STA UNI"
Pragma: no-cache
Server: Apache-Coyote/1.1
Set-Cookie: vglnk.Agent.p=5a49e2c7f52a8ad48bba0d780e671075; Domain=.viglink.com; Expires=Fri, 17-May-2024 10:42:05 GMT; Path=/
Vary: Accept-Encoding
Content-Length: 31
Connection: keep-alive

jsonp('http://bit.ly/1gf00Wo');

two favicons requests here.. and finally:

GET /1gf00Wo HTTP/1.1
Host: bit.ly
User-Agent: Mozilla/5.0 (Android; Mobile; rv:29.0) Gecko/29.0 Firefox/29.0
Accept: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
Accept-Language: it-IT,it;q=0.8,en-US;q=0.5,en;q=0.3
Accept-Encoding: gzip, deflate
Referer: http://link.tapatalk.com/api/click?key=a7e5ffb24b9e84f4f4f6bbd88aa4e5b8&out=http%3A%2F%2Fbit.ly%2F1gf00Wo&subId=c157297d1a1ff043255bfb18530caaa2
Cookie: _bit=53582465-00123-03e61-311cf10a
Connection: keep-alive

HTTP/1.1 301 Moved Permanently
Server: nginx
Date: Tue, 20 May 2014 10:42:06 GMT
Content-Type: text/html; charset=utf-8
Connection: keep-alive
Cache-Control: private; max-age=90
Content-Length: 134
Location: http://www.youtube.com/watch?v=dQw4w9WgXcQ
Mime-Version: 1.0

<html>
<head>
<title>bit.ly</title>
</head>
<body>
<a href="http://www.youtube.com/watch?v=dQw4w9WgXcQ">moved here</a>
</body>
</html>

i can send you the apk within 1hour if you need (now i'm supposed to be working :) )