The Big Easy15
Score 1,000,000 points in Arcade Mode
See Well Hard
Score 5,000,000 points in Arcade Mode
See Well Hard
Score 10,000,000 points in Arcade Mode
Difficulty is not important. Doing this on Easy will take more time, but it is far more manageable. Not super quick, but much easier.
Defeat your first Guardian
Can't miss this one. Kill parasites until the rage meter on the bottom of the screen fills up and triggers the Guardian. Circle-strafing does make it more simple. If you still have problems, a smart bomb will lower a lot of the health.
Defeat 10 Guardians in a game
This is pretty self-explanatory. Ten in one game is not terribly difficult and should be done on Easy just for the sake of simplicity.
Defeat 250 Guardians in total
This is a significant grinding Achievement. The best way to do this is to:
1) Kill 20 Guardians in a single game on Easy. It unlocks Overkill mode, which allows you to play with all weaponry and unlimited smart bombs. Overkill makes all of the killing Achievements easier.
2) Play Overkill for however long it takes to pull it off. Took me about 2 hours. Pursuing this will also help you in working towards Grand Master.
Raise the score multiplier to 5x
This is the only Achievement you cannot do in Easy. Medium's first few levels aren't all that difficult, so it shouldn't be a major problem.
Bounce 100 enemy bullets with an upgraded shield in one game
The easiest way to handle this is with the Guardian battles. After you get the shield upgrade, on your next few Guardian battles, simply reflect the mass of bullets they will normally unload on you before putting up their own shields. Of course, if they use the laser or the arc, avoid it --- but most will fire tons of bullets at you and it's fairly easy to reflect them. Just face where the boss is.
Destroy 20 Hunters in one game
A Hunter will come to attack you if you do not trigger a Guardian encounter within a time limit. By and large, it usually is after your point multiplier lowers. It's a quick little star-shaped enemy that will go after you. This, like most of the Achievements involving killing a set number of enemies, is easier to handle in Overkill mode. Much easier to kill Hunters with unlimited smart bombs.
Squash 111 harmless enemies with your ship during one level
After several Guardian encounters, you'll notice tiny little specks on the screen. If you hit one and your score goes up, you're hitting a harmless enemy. Just fly around and squash them. They look like specks of dust, but you do need go through several encounters before you will first encounter this.
Smarter Than The Average Bomb25
Destroy 50 enemies with one smart bomb
Also highly recommended to use Overkill mode. It will take, roughly, 20 encounters before killing 50 with one bomb becomes fairly easy. It can be done earlier, but it gets progressively easier the later you go and Overkill makes it much easier.
Destroy at least 1000 of each enemy type
No trick for this one. Overkill is your friend. You must kill all enemies 1,000 times --- including Guardians and Hunters, so this is going to be a long grind. Overkill allows you to fight an unlimited number of enemies with unlimited smart bombs, so if you can sacrifice the hours needed to pull off, do it.