I have reached map 58 by using a backup and restore app. My Nexus 6 is rooted and by using Titanium Backup, when I reach the sector before the last one on a map, I exit the game and back it up. I then reenter the game and attempt the last sector. If I fail, I exit the game, do a data only restore, then reenter the game at the next to the last sector, ready to try another strategy.
My fleet consists of three Valiants. My flag ship is armed with 4 death rays with recycle times of 6, average hull damage of about 1300, average shield damage of about 750. One of the other ships is armed with 4 laser cannons with average recycle time of 4, hull damage of about 620, and average shield damage of 1250. My last ship is armed with 4 mega plasma cannons with an average recycle time of 5.1,average hull damage of 1250, and average shield damage of about 2900. All ships have one hangar bay devoted to shield repair drones and the other to hull repair drones. The point defenses on all three are 2 lasers and 2 bolters, the rest filled with shield boosters. My formation is side by side with the flagship in the middle and slightly behind. I have found this formation best most of the time. The reason is that I found that if you get the ships to cross over each other during the battle, their shields become cumulative, and protect each other. So, every time I warp into a hostile sector, I press pause, break formation and have the ship on the right head dead left, and the ship on the left head dead right. I also target the furthest enemy ship with my plasma cannons, because the nearest one is automatically targeted for everything, but by the time the plasma gets there, the ship has been destroyed by beam weapons. This way your plasma cannons can be much more useful.
Some bugs I've noticed.
Tiny fighters being targeted by multiple beams, but not getting destroyed until hit by something solid.
Plasma and beam weapons continuing to fire at enemies after they have warped out.
