Assault Suit Leynos

Once you reach the giant boss ship in stage 1, a countdown timer will appear indicating how close the ship is to your base. To earn this trophy you must destroy the boss ship before the countdown timer reaches 45. This may be easier to do in Classic Mode, because in Arcade Mode the camera will pull away from you to show the boss approaching. You can still shoot while this is happening, but it's hard to know where to aim your gun when you can't see yourself on the screen.

For the easiest time with this, equip the D-D weapon and begin shooting immediately when the countdown appears. Alternate between the D-D and the LG-GUN, keeping track of the ammo count in the latter. As soon as it empties to zero, switch back to the D-D so you aren't wasting precious seconds while the machine gun reloads.

If you're going for this trophy in Arcade Mode, unequip the 25-SC to save time on weapon swaps. Get to the end of the stage as fast as possible so you're right there when the boss ship appears. Start with the LG-GUN and have the laser sighting equipped from the options menu (it unlocks eventually after you earn enough points from your total play time). This will let you see where you're aiming so you can get in some shots while the camera is still focused on the boss ship. Then when it returns to normal view, switch to the D-D and begin alternating between the two weapons.

The timer will continue counting down as the boss ship crashes, but as long as its life bar is completely depleted before the counter reaches 45, you will earn the trophy.