I think the fastest way to do this:
Method 1: If you already have a vector
- Add some white shapes on top of your graphic to hide the details.
- Then open the "pathfinder" panel, select all and "divide" everything.
- Then select at a piece of white, go in the menu "select" and choose "select same fill color". And delete the white parts.
Method 2: In Photoshop or Gimp, then vector
Simply use the selection tool and fill the details areas with white. You can also use a brush if you prefer. This should be very quick, especially with the polygonal lasso tool to select the extra details.
Then copy/paste that image in Illustrator and use the command "Trace", adjust the settings to your preferences, then press "expand" to make a vector out of this graphic.
- If you want to soften the edges, you can add a stroke with a "round corner" and manually fix what you don't like.
I don't know if there's still too many details in this example. You can fix this manually and quickly if you don't want to retrace everything and if you want to keep the asymmetry of the tracing.