How to scale a high-load site (Python, MySQL)?

There is a working site written in Python (Django), and the database is MySQL.
Since the developers did not work much on writing optimized code, the site turned out to be very heavy. And with tens of thousands of visits per day, at peak times, the server cannot handle the load and drops those it couldn't serve.
Here is the physical server configuration:
1. 2 cores at 1.8GHz
2. RAM 2GB

What is currently deployed on the server:
mysql + nginx + fastcgi

So the question : I would like to hear the opinion of experienced people, or simply those who know, what can be expanded on this site to make it as fast and resource-efficient as possible? Or is this a dead end?