So I need to create a graph that basically looks like an ascending line graph.
on the x-axis will be time, and on the y-axis will be achievements that the user has unlocked.
Each achievement shown will be a specified height above the previous, and a certain distance across the x-axis depending when they were unlocked.
What would be the best method to accomplish this?
You can use HighCharts. Or, Raphaël for a more powerful solution. These libraries works using SVG.
Here there is an example using HighCharts.