After winning 99k in stock market I upgraded my banshee for 45k+
Below is the cheapest alternatives for the Banshee vehicle. Since I had 99k I chose chrome paint and better looking wheels. Its up to you how much you have, you need atleast 40000. You can spend 20000 by upgrading a low class vehicle like the Weemy Issi Compacts (Mini Cooper) credits to Chrisli128's comment.
Engine--2340 (Level 1 engine)
Hood--680 (Carbon Hood might be needed)
Respray Primary Classic--320 (Chrome paint might be needed)
Respray Secondary Classic--160 (Chrome paint might be needed)
Wheel Accessories: Custom, Bulletproof & Smoke--1000,2000,1200 (you need all these different parts)
The above is for the Banshee car. Other cars may have different parts like Skirts, Stairs, Roof. Make sure to buy those as well. Exit the shop and achievement unlocks.
You need all color options and accessories then achievement unlocks.
Make sure none of the options is stock.
If achievement don't unlock go back into the Los santos customs and buy some more parts, change the paint colors and see if it unlocks then.