You will have to change the HTML markup.
Try with this CSS:
#mega-menu {
display: none;
position: absolute;
left: 0;
z-index: 1;
}
#mega-menu:hover{
display: block;
}
#trigger a:hover + nav {
display: block;
}
And this HTML:
<!--Navigation-->
<nav>
<div class="nav-wrapper teal lighten-2">
<div class="container">
<a href="#!" class="brand-logo"><img id="logo-img" class="responsive-img" src="img/main-logo.svg" /></a>
<a href="#" data-activates="mobile-demo" class="button-collapse"><i class="material-icons">menu</i></a>
<ul class="right hide-on-med-and-down">
<li id="trigger">
<a href="index.html">Home</a>
<!--Secondary Mega Menu-->
<nav id="mega-menu">
<div class="nav-wrapper red lighten-2">
<div class="container">
<ul class="left hide-on-med-and-down">
<li><a href="index.html">Test</a></li>
<li><a href="badges.html">Test</a></li>
<li><a href="collapsible.html">Test</a></li>
<li><a href="mobile.html">Test</a></li>
</ul>
</div>
</div>
</nav>
</li>
<li><a href="badges.html">About</a></li>
<li><a href="collapsible.html">Blog</a></li>
<li><a href="mobile.html">Portfolio</a></li>
</ul>
<ul class="side-nav" id="mobile-demo">
<div id="mobile-logo"><img class="responsive-img" src="img/mobile-logo.svg" /></div>
<li class="active"><a href="index.html">Home</a></li>
<li><a href="badges.html">About</a></li>
<li><a href="collapsible.html">Blog</a></li>
<li><a href="mobile.html">Portfolio</a></li>
</ul>
</div>
</div>
</nav>