Here is the full list of all 15 Darts Up trophies - there are 3 bronze, 1 silver, 10 gold and 1 platinum.
Get all the trophies
Throw Three times on the Triple.
Get Three Doubles in the same round.
Throw Three Times on the Bulls Eye.
Throw on the Triple 20 + Triple 1 + Triple 5
Throw on the Triple 6.
Throw the dart on the Center
Get 45 Points in the same round.
Throw the dart on the Double
Complete the Level 5 in Arcade Mode
Complete the Level 4 in Arcade Mode
Complete the Level 3 in Arcade Mode
Complete the Level 2 in Arcade Mode
Complete the Level 1 in Arcade Mode
Throw the dart on the Triple