This is a video for this and the blademaster achievement:
If you play through this mode, without consulting guides and just trying to keep the score multiplier high, you probably won't manage to get 1,000,000 points.
The basic and most effective way to get these achievements is to parry everything and use maelstrom on bosses, below I've given explanations and tips:
-Parrying: you probs didn't even come across this while playing the episode, but if you block an enemy’s attacks (X/Square) at the right time, you parry it by pressing B/Circle when prompted. This gets you a stupid amount of points. Easiest way to parry is to hold the block button in for 1 second, release and repeat until you can parry. It's a very poorly designed mechanic, so it would be very hard to perfectly time each parry, but you could watch them and hold block 1 sec before their attack lands.
-With all basic enemies (non-bosses) you should aim to kill them via parry. If you notice you are losing a lot of time and you just can't parry, kill them normally and try again with the next set.
-Bosses: you want to parry them as much as possible but also ensure to use at least one FULL maelstrom on each of them (that includes the Y/Triangle QTE prompt), the final combo gives a huge amount of points (if they die before the hit, you won't get those points, so consider using it earlier). You also need to be very careful with damage, as using items, will award you less bonus points. Watch the way I fight them for tips.
-Items: you start with a sizable amount of items. Do your absolute best to use none at all. However, use potions over anything else, as using a phoenix down will deduct bonus points. When you complete the score attack, you will receive bonus points for the remaining items you have at the end of the Gilgamesh fight. I believe I used 2-3 potions and possibly a phoenix down, and I received almost 120,000 bonus points. So that can give you an idea how many points you want to have by the time you kill Gilgamesh the second time.
-Time Limit: Each round (ending with a trial), is given a time limit, all 10mins, except for the third trial, which gives 15 mins, due to its length. You will notice in my run-through, I had heaps of spare time, meaning if you are struggling with parry's, you can allow yourself a bit more time. I highly recommend not wasting too much time in the third trial (starts after the fire bird and ends with iron giant) and killing enemies if you can't parry. The iron giant boss takes a huge amount of time and since you want to avoid damage, you need time.
-Tips for bosses:
*The Snake: is very simple, use a Maelstrom and then parry to death.
*Fire Bird: I recommend using a Maelstrom and attempting to parry, if not use pillars and try to charge another Maelstrom.
*Wall Demon: Maelstrom(s) and parry the other enemies, he will likely be damaged by the splash damage and then focus on him, when other enemies are dead.
*Iron Giant: Maelstrom straight away, then try to parry and get the rage meter up (by defending), rage meter will increase dealt damage. If parrying is causing you to take too much damage, use the pillar, then defend, attack once and rinse and repeat, the rage meter will avoid it taking too much time. If he turns red, just dodge roll, you can't parry. I also recommend not using a second Maelstrom if he is close to death, as you can use it on Gilgamesh and gain more points and possibly make the fight easier, if you struggle.
-Gilgamesh: You can parry his attacks, but he turns red often, which then means you can't parry. Once he turns red, dodge, attack once and repeat, until you can parry again. Use Maelstrom as frequently as possible (it can damage him up to half health, depending on rage meter).
**I highly recommend watching how I do each of these fights, after reading this, as seeing it, will really help to improve your performance