For this achievement you will have to survive for 8 minutes in one game. As you play this mode you will get better at it. Kill enemies without putting them into Manic mode to make it easier, or take your chances if you are wanting to get the 300,000 points. You must play Infinite mode for 8 minutes, but this doesn't mean you cannot die. As long as you play in one session, you should get this achievement really easily.
Note: During a few of the boss battles, you may notice that if you just sit in one spot, their bullets will not hit you. And it does not change pattern, so you can pretty much just stay near a corner where bullets are missing.