Try hitting F4 and read the additional mission directives as they're added, for a hint. It's not spelled out for you, but there may be enough to get an idea of what you're being asked to do. I didn't realize they were there until I was already done, though.
For the giant mecha:
There's a pair of GTS Hygeias, somewhere. Now, think about a bodily region of which seemingly about half of
America's Funniest Videos clips involve injury to. (i.e. they're not eyes)
If that's not enough(or you're not from the USA, and thus may have no idea what I'm talking about), check the Hades' fighterbay.
How to end the mission?
My recommendation is to grab the 'star' powerup as you dash to the Knossos.
It is all completely doable without cheats; there's often a weak point or little 'gimmick' you have to do/perform to finish the task/mission, but it's all doable.
