The first and oldest way is to simply design and assume the Achievement this is the way the first "Coat of Arms" came into existence and is still a legal way to gain them.
Where did you come by that particular legal nugget...? My understanding was that, technically, apart from inheriting them, they could only be granted by the Crown or the College of Arms or otherwise be acknowledged by the College (eg by prescription). The other problem would be finding out if the design has already been used: even the College of Arms, although no doubt extensive, doesn't have a
comprehensive record of all of the arms ever used (in England and Wales).
Of course, "legal" is a bit ambiguous here (at the risk of repeating a previous post of mine). While technically correct that it's illegal to assume arms to which you're not entitled, in England, Wales and Northern Ireland, it's neither a criminal nor civil offence, but a chivalric offence - and the Court of Chivalry hasn't existed since 1737, in part precisely because it lacked comprehensive records and was open to challenge (except for one case in the 1950s, which today would have been covered by modern legislation). Certainly, the legal basis on which to challenge a private individual's use of arms is today as good as non-existent, which undermines the notion of a "right" - rights are worthless if unenforceable, however much you've spent with the College of Arms or however nice that parchment looks.
The coats of arms used by local authorities are interesting in that respect - although they have to be granted by the College of Arms, they're also protected legally by local government legislation in the 1990s, so strongly suggesting that a grant from the College of Arms isn't enough to enforce their legal right. There was a case not too long ago in Kent where a local authority was forced to change their arms because they'd wrongfully "inherited" them from a previous authority that no longer exists - even the local football team had to change their shirts because of that.
