Yes, you can manually implement Isotope and it’s pretty easy if you have some little knowledge of HTML + JavaScript and sometimes PHP if you need to pull some taxonomy data for example.
But as @MartinWB says Isotope is cool if you already have all the posts in the page in a single load. If your site don’t have a lot of posts or you just cache your posts and you don’t update them too much, Isotope is a cool solution.
But for something more sofisticated the AJAX method is the way to go.
One thing that can help with filter speed in AJAX is an Object Cache. If your hosting allows it, it’s an easy way to improve your filtering speed.