Upload & Sell: On
A light box will give very soft, even lighting all around, and eliminate reflections of nearby objects in the room from the metallic surface of the trophy.
You can get a similar effect by using flats of foam core or card stock, bedsheets hung from a frame of some kind, etc.
If you have a sturdy tripod, you can also shoot multiple frames, moving your umbrella or softbox for each shot, and combine them in post processing for the best look. (The soft box will probably work better, with its smooth, symetrical face. Umbrellas can sometimes show their ribs in reflective objects.)
Available light can work if you can avoid shadows cast by the reflection-masking setup.
You can also make a light box pretty cheaply: