Complete the game with any Lion.
This trophy will be earned through normal story mode. Once you have completed Doom 4, the credits will roll and you will have finished the game and earned this one.
Complete the game with all five Lions.
At first look, I thought perhaps this was an online trophy. As far as I know, it is not. Simply playthrough the game 5 times, once with each lion and this trophy will pop when you finish Doom 4 with the fifth lion. There is a shortcut that can be taken also to obtain this one quicker. Once you have beaten the game once, you can use level select and play the final board as each lion to unlock this even quicker than through normal gameplay. Thanks to MythicalChick for this tip.
King Alfor's Blessing
Get five Survivor bonuses in a single play session.
This one you may unlock in the later levels, I popped this one in the Yadle areas. When your robot lion is damaged to the point where it's health bar is 0, your pilot will be ejected and a countdown timer will appear above your lion. This is what they call survivor mode, as your pilot is armed only with a pea shooter laser, and the goal is to survive for 10 seconds while your lion is repairing itself. Once the timer counts down, if you can make it back to your lion without dying (1 hit can kill you). You will get a 10,000 survivor bonus. Achieve this five times in one level and this trophy shall be yours.
Defender of the Universe
Rescue 100 groups of civilians.
This is a collectible trophy. You will notice in Arus 2 and later on in the part 2 and 3 levels that there are groups of civilians waiting around in blue circles. Collecting these will add to your civilian count, and also increase your health, should you have taken damage and need a bit of healing. I had around 60-63 when i finished my first playthrough. So I find that a second playthrough is necessary, as it continues the count of civilians, even if you have completed the game once already. Also worth noting, is when you are on Doom 3, when you are escorting the transport ships, once they have reached their destination, you can collect them as civilian rescues. Once you have rescued 100 civilians, this trophy will pop.
Complete any level without the Lion deactivating once.
Once you get the hang of the controls and weapons on your robot lion, this trophy should not be hard to unlock. Go through a level and ensure that you do not lose all of your energy to the point where your pilot is ejected from your lion. This is what is known as "Survivor mode". If you can avoid this for one complete level, then once the level completes the trophy will pop.
Complete a level in an online game with four other players.
This is an online trophy. You are required to play a level online with four other players. Once you have completed a level with all 5 lions, then this trophy will pop. I also find that if you are hosting the game, then it is a bit easier to wait for the other 4 players, then you can start the match and work towards earning this one. I am currently boosting this trophy, and can also help with any of the other online ones.
Complete any three levels without seeing a game over in a single play session.
This trophy can be unlocked in single player or multiplayer. Probably a bit easier to get it in single player. Go through 3 consecutive levels without losing all of your 5 lives and seeing the game over screen. (And Haggar laughing at you), and this trophy will pop once you see the level complete screen for your third level. I popped this one on Arus 3.
Achieve ten air pounces in a single level.
This trophy can be achieved in the first level of the game. Once you get past the initial tutorial stages, you will encounter flying scorpion ship enemies. If you point your lion towards the direction of the flying enemy, you will see a lock-on target automatically show up on the enemy. The issues though is that you must pay attention to the flying pattern, and be careful if you are shooting, as your lasers can also hit these enemies and you want to pounce on them with R2. Achieve 10 takedowns in one level, and this trophy is yours.
The Vendetta Begins
Beat a friend's level score after they have beaten yours in the same online game session.
The second online trophy. In a multiplayer match, you will want to play a few levels together. This trophy requires you to have your friend achieve a higher level score than you upon completing a level, and then in the next level, you need to beat that level score. Upon doing all this, this trophy will unlock. I found this one to not be very hard at all, as the levels progress, there are more enemies and more chances to rack up mad points.
Carried the Team
Complete a level in an online game where you are the only surviving player.
Another multiplayer trophy. This one can require a bit of skill on the trophy earner's part. When playing any multiplayer match, all lives are shared between all players. The goal for this trophy, is to be the sole surviving robot lion, and to complete the level. I popped this one on either Yadle 3 or it was one of the first two doom levels. Other players will respawn when the next level starts up.
Earn a x10 score combo five times in a single level.
This should be another easily obtainable trophy. Chances are you will get it either in the later Arus levels or in the Yadle or Doom levels. When you are being bombarded by enemies and the fighting is intense, you will notice that once you start shooting several enemies at once, it will begin giving you a multiplier for the multi-kills. You must shoot quickly to keep the multiplier going. Once you reach x10 multiplier, let it count down a bit and then back up to 10x, and this trophy will easily pop.
Kill a Robeast without Voltron losing any health.
This trophy requires a bit of timing and patience, and a touch of practice. Once you get the hang of the Voltron battle levels, then this should be an easy trophy. When you are fighting the robeast, you must get either a perfect attack, or attack successful, as well as not miss any defense bonus attacks. Easiest beast to pop this one on, is the robeast from Arus 4, however, if you really want to challenge yourself. It can be achieved during the fight with the Zarkon robeast also.