The expression contains two words:
- бряцать – to rattle
- регалиями – stems from regalia, but more like medals here
The figurative meaning is to show off one’s life experience. I.e., in an argument, instead of providing logical rationale behind one’s position, to stress an argument from authority and/or “superior” life experience.
As an example, the expression could also be used in a context where someone (say Alice) wants to get a better deal for his/her acquaintance (say Bob) from a third person (say Charlie). So Alice could come to Charlie and ask for a favour showing off all the past favours she did to Charlie. In this case, Charlie could say jokingly “You do not need to rattle your medals here, I was going to propose a discount anyway.”
In this example, the metaphorical regalia are not past favours that Charlie had from Alice and now she wants to redeem them (like coupons). No, it is more like Alice thinks she has some intangible leverage (as opposed to tangible, like a gun or a pair of goons by her side) which in her mind is enough to ask for a favour. Again, could be used jokingly or seriously.