2005 Hyundai Tiburon Car shakes when accelerating

The motor mounts may be bad. You can check this by opening the hood and getting a line of site on the engine. With the parking brake on give it a blip of gas and see if the engine moves more than a half inch or so. If you replace motor mounts you must replace all the mounts and the transmission mount all at once or the older mounts will quickly fail and then break the new mount.

Sorry I wasn't clear the first time. :(. When its in idle n I hit the gas it goes away... But when I'm driving and usually when accelerating it vibrates, almost feels like it shakes... If I let off the gas or just stay at a steady speed it stops.. Only when I hit the gas is does it.

It could be a combustion issue. Things to look at are the compression and maybe the EGR valve. You might also check the fuel pressure. However I still think the motor mounts are suspect. Below is a link explaining vibrations;

https://www.2carpros.com/articles/engine-vibration-at-idle

Hey, I changed the mounts and still the same vibrations. For some reason sometimes it's hard to shift into gears. I will have to wait until the rpms drop. I'm so lost lol. I just want to figure it out. Please help

It could be the input shaft bearings on the transmission have gone bad.