I've never owned a eugenia but I've seen them around. Instinctively, I would trim off the dead and dried branches. Take care to see if there are leaf nodes that are viable. When revived, these would start to sprout and produce stems. It may take a long for a regrowth, so be patient. When new stems develop let it grow out a bit and simply nip off the tips to force it to branch out. Keep nipping over time until you get to shape it to a ball. This may take a long time to do so please keep that in mind. If there's not regrowth at all and the branches are all dead, trim them all out. You can get the lower and top ball to grow wider to minimize the gap in between so it starts to look good once again.

Hope that's a start. I have a bay tree which I'd began to shape into 2 lollipops when it was a mere 1 foot plant. At this time, you would not be able to discern the balls because the stem growth is slow, but it's getting there. It's now reached 5 feet and I've just nipped off it's top to force out side branches. It doesn't look impressive but in 2 years it would look great.