He already figured out Diamond for Burger, but so people know:

You need to be on easy mode, and you need to run out of keys (if you've just restarted the game, pick up and use at least one key). Then at the top of the screen you'll see a timer countdown 60 seconds. If you click that timer you will be offered to pay 1 soul stone to instantly get the 1 yellow key. If you do it, you get the achievement.

ALSO like RPGamer05x asked, can you exchange soul stones and still get penny pincher? (soul stone =/= money)

I tried only with soul stones and i still dont get the achievment

This is a late reply, but in case someone still wants to know how to get the Penny pincher achievement:

You can:
- buy attack/defense from altar
- use soul stones to restart a zone (and probably also resurrect after dying, didn't try this)

You can not:
- buy anything from people (keys, scrolls etc)
- buy from soul merchants (on levels with altars)

I don't know if speeding up the free yellow key with a soul stone voids the achievement. It's not really a problem since it's possible to wait instead.