To obtain this achievement you must defeat the hidden boss Fainter that appears at the end of Stage 3. This will require a specific amount of total points score in order to achieve so avoid dying at all costs.
By the end of Stage 3, make sure you have roughly 2900 Total Points by the time you get to the EMERGENCY prompt. Just anchor everything you see and shoot at ground enemies or in this case enemies on a revolving ring. Towards the end of the stage you will face ships that will shoot LOTS of projectiles in a variety. Be sure to anchor and throw them at each other as they appear on screen or you will get overwhelmed. There are 6 in al, sol be sure to anchor the 6th one and hold on to it for the boss fight. Once the fight starts, let go of it at the boss. This will not destroy the 1st Form of the Boss, but it will give you a head start in damage. From there simply finish the 1st Form with lock-on shootingForm 2:
The boss will begin to shoot out projectiles very rapidly dodge them at the best of your ability or just shoot at them if playing on EASY. If you have around 2300 points or more you can take it down with gun fire but beware of bullets and use bombs to save your life.Form 3:
Simply anchor the white mini ships from the right or left sides that appear and launch them at the boss for the finish. Make sure you have 3000 total points by now. If done correctly Faintear will appear after the Boss is destroyed.Stage 3 Faintear(2 Forms)
Form 1: She will shoot bullets in a circular motion(similar to Stage 1)and you need to dodge these until she brings in red ships that surround her. Anchor one or two into her to defeat her.This may take a few tries if your aim is not that good. Make sure you defeat her fast because the longer it takes you to beat her the more bullets she will fire.Note:
Form 2: Faintear will close in on you and bring out a rotating shield with 4 mini ships in each corner of it. It will begin to rotate and shoot vigorously, you may have to dodge bullets while moving around her here. Use the "Pause Trick" here and dodge the bullets. Try anchoring one of the mini red ships and hurl it at her. If she does not die try waiting for the revolving lasers to die down then cross over to another section of the shield and anchor another ship until she dies. The shield itself is anchorable too if you prefer to beat her that way.
This video will show you the entire playthrough of Stage 3 and it also includes the hidden Faintear fight. Pay close attention to the Total Points needed in order to face her and the strategy used to stay alive.