When selecting the Millennium Tower stage, select "No" when asked to use the boot-up key. Plain and simple, you need to clear this level by defeating the enemies and the final boss.
Equipping both characters properly is key to doing so. By giving certain bonuses to your characters through equipment, you'll have a much better chance of surviving the onslaught of enemies.
You can only equip up to five different equipment bonuses - anymore than that will not count. Items that provide the same bonuses will not stack (or work together). With these restrictions in mind, I recommend looking at all your equipment and going with the following:
- Hit point bonus
- Hit point regeneration
- Attack bonus
- Element (of your choice)
These bonuses will make it much more manageable. Continue through the level like any other. Use health drops wisely, making sure both your character and Alisa get enough healing.
The hit point/defense bonus and regeneration should help with any damage you'll take. The attack and elemental bonuses will cut down time needed to defeat enemies.
Upon defeating the boss at the end of the level, you will earn the achievement.