The hard rules are the ones that overlap
A rule becomes hard when its characters also affect other rules. Roman numerals are difficult because they use ordinary letters. Digit sums are difficult because many unrelated rules require numbers. Prime length is difficult because every edit changes it.
The Password Game is less about solving one hard clue and more about keeping many small systems stable at the same time.
Where players usually get stuck
Many attempts slow down around the middle of the game, when the year, binary string, country name, and uppercase-vowel requirement interact. The final stage can be even tighter because length and ASCII totals force careful one-character tuning.
When you get stuck, reduce the password to parts you understand. Identify which part solves each rule, then adjust only the part connected to the failed rule.