Side Vower is a bit more difficult than the Stranian side and you'll be playing the game in reverse stage order, like Stage 6 is Stage 1 and so on. It'll take some skill to earn the "Perfect Conquest" Achievements in Side Vower. Its also unstackable and has to be done on the default lives setting. You can also earn these in Co-Op, provided you have a skilled partner that can help you get them in a true 1CC (1 Credit Clear) setting.
Note: If either you or your partner happens to lose all lives and not continue and either you or your partner complete the entire playthrough without losing all lives, you and your partner will both still earn the respective achievements for whichever Difficulty you chose. This also works on the Stranian side as well.