It looks like a 40-pin 3.3V display.
Buy a 40-pin TFT adapter shield for Mega2560. Then use UTFT Llibrary.
You end up with a 3 layer sandwich i.e. Mega + Adapter + Display.
You can buy 2.4" Uno shields for about the same price as the Adapter.
These are 2 layer i.e. Uno + Display
David.