When you get to the boss you just have to take his energy down so far and then he'll come to you to activate a sword fight sequence, what you need to do is press x as fast as you can to defeat him, whereas originally i just pressed x when it came up so would die.
Act 1:
Mission 1: Landing
Mission 2: Breach
Mission 3: Giant
Mission 4: Rescue
Mission 5: Trust
Mission 6: Darkness
Mission 7: Seismic
Mission 8: Hostile
Story related achievement BUT it can be missed!
Warning:
"Complete all Acts" requires playing through all Acts consecutively. If you use mission select at any time in your playthrough, you will not get the achievement for completing the game even though you have literally completed all Acts and have the achievements for each Act! You won't unlock the Living Legend achievement either!
The same applies to "Complete Act #". If you use mission select before having finished an entire Act, you will not get the achievement related to completing that particular Act. (Thanks to vithzeral for pointing this out).
When you use mission select, even after you have beat the game, all your weapons will be set to standard settings without any upgrades!
Courtesy of
http://www.xbox360achievements.org/game/vanquish/guide/