There are 2 ways to go sunward. You can shed speed to reduce orbital distance, but 30 km/s is a lot of velocity to change. Or you use another body (often antisunward) and a slingshot to put the craft in a highly eccentric orbit that, at times, is near the sun - so you have many proximal destinations you have to hit without error to meet your course. A mars transfer is easier but you want to hit certain proximity windows.

From my knowledge in KSP, in a nutshell if you pass by a large gravitational mass on one side you'll speed up, but if you pass on the other side you'll slow down. Throw in an engine burn across the periapse (closest point) and you'll amplify that much more.