A double eagle is scored any time you finish a hole at three under par. A double eagle is also called an albatross. This trophy is highly dependent on luck. In order to score a double eagle on a par 4, you must hit a hole-in-one. On a par 5, you must be aiming for the pin on the second stroke. It is not possible to obtain this trophy on a par 3.
Once again, Maple Leaf Golf Club (Challenge 1-1) is the easiest course to obtain this on. Holes 1 (par 4), 3 (par 5), and 9 (par 5) all provide an opportunity for a double eagle. You will want a character with high power, high control and decent impact.
NOTE: I recommend not trying to grind this trophy until the very end. Due to the high degree of luck required for this trophy, you may want to combine this attempt with Go for the Ace! so that you don't have to hope for lightning to strike twice. You'll need a par 4 that is short enough you can reach the pin from the tee. The best options are Maple Leaf GC Holes 1 & 4, Kagurayama CC Hole 2, Harvest Hills GC Holes 3, 4, & 13, and Mt. Sakura CC (DLC) Holes 15 & 18. In my opinion, the best option is Kagurayama Hole 2 because it has several cup positions in the section of the green that you are most likely to hit, and it doesn't have small unpredictable hills in front of the green like Maple Leaf Hole 1 (which would be my second choice). Also, both of these options are early enough that you can quit and retry without spending too much time/effort trying to get to them.