When you finally leave your hotel room, you will end up with some matryoshkan cash as part of the main storyline. Give money to all personel in the hotel lobby/reception area. The two at the reception, one at the luggage counter, one at the money exchange, the security manager and the bellhop. The last wasn't needed for the achievement to pop for me, which could mean 3 things:
1. You need to bribe 5 ppl
2. I tried to bribe him when not focusing on the achievement
3. It carries over between playthroughs
4. He just isn't included in the achievement.