Can I do the Courier Who Broke The Bank trophy without having to waste money gambling.
Can I attack people and get kicked out? If I put mines averywhere and massacre every unamed npc there will I get kicked out? Because no way in hell am I going to win anything! Rouletes bulls**t. Your're not meant to win that. Blackjack, forget it.
No I am not wasting my time gambling unless I have to.
So can you do it but killing npcs?

Uhh ofc you have to gamble. that's the whole point of the achievement

Thats what breaking the bank means, aka winning so much they ban you.

A high luck skill is needed unless your strategic at blackjack. Because luck affects criticals I keep it high with all characters but if yours is low then yes it can be hard to get the achievement. Killing everyone won't do it. So yes you have to gamble unless your on the PC.

Frag it. I hoped that getting banned might mean behaving badly. The trophy says get banned not gamble yourself to a ban spercifically. F***ing gambling. Total waste of time and money. I'll have to throw all those NCR dollars and denarius I got from killing CL into the sewer via gambling. No way in hell I am using my caps.

Build up your luck and then play blackjack. Skip roulette and the slots completely, except for the number of plays (10 each, IIRC) you need to get the achievements for them, and bet small on those. Blackjack's simple to play, you can master what strategy there is really quickly, and with high luck you'll soon be getting banned from all the casinos. But breaking the banks is the only way to get banned.