Collecting all five gems is the single highest-leverage late-game quest in Ice Tycoon 2. The Collector badge awards a permanent upgrader that carries over through every rebirth.
Most players solve the gem hunt in the order Yellow, Blue, Green, Purple, Red. The Yellow gem in the hotel vent shaft is the easiest, while the Red gem behind the lava exhaust valve is the easiest to miss.
Pair the gem hunt with the Secret Finder badge. The three riddles stack a permanent +5% cash yield each, compounding with group and premium bonuses.