I want to be able to create a anti-aliasing effect as shown in windows command prompt with any text or vector I'd like without having to screenshot it within the program. How could I go about doing this?
Not a result exactly like your example but you could do like this in Illustrator:
Now the result can be a bit unpredictable with shadow not appearing on some letters so one need to tweek and experiment.
In Illustrator, using the free LomoCopy LT Std Midi font:
Over a black background type the text and use the Appearance Panel to add a light fill color with a lighten blend option:
Duplicate this fill, change the color and from the menu Effect → Distort Transform → Transform → move it horizontally to the left:
Duplicate this second fill, change the color and double click Transform → move it horizontally to the right: