I just googled Achingal and a place called Achingale, near Wick came up on an estate agent website. www.georgesonsproperty.co.uk.
Also on www.scotlandsplaces.gov.uk
there is an Achingale Mill
They are in the right part of the country so may be of some help.
Wick is a very long way from Cullen in early 18th century terms, and by no stretch of the imagination could this Achingale near Wick be or in even near the parish of Cullen. If the people involved had been resident in a part of the country so far away, the parish clerk would normally have said 'Achingal in the parish of Wick' or whichever parish it was in. I am willing to bet that this Achingale in Caithness is a complete red herring.
The record you quoted seems to come from the Cullen parish register, and the parish of Cullen was quite small in area, so you can be confident that wherever it was, it is very close indeed to the present town of Cullen. The parish of Cullen extended about 2 miles north to south and 1 mile east to west, before it was enlarged by the addition of a quoad sacra annexation of 3 miles by two miles, which includes the village of Portknockie. I do not know when the annexation was added to Cullen, but it was before the 1790s, because it is mentioned in the Statistical Account. It would be very relevant to know when this happened, because if it was after 1722 you can be sure that James Taylor and Ann Hay both lived in the two square miles of the original parish of Cullen proper.
Achingal may even have been obliterated by the present town, because the upper town was built in about 1830, so it didn't exist when James Taylor and Ann Hay got married in the parish over 100 years before. 'Cullen' in the 1722 marriage record will refer to Old Cullen, a small village in the parish of Cullen close to where Cullen House now stands.
If you really want to find Achingal, your best bet would be to take a look at the Seafield Estate papers. These are in the National
Archives Records of Scotland in Edinburgh - but be warned, there are 2½ tons of documents in the Seafield collection. (In spite of the amount of paper it is possible to find gems in it - I found a letter written in his own hand from my umpteenth-great-grandfather to the factor making an offer for the tenancy of a farm on Seafield land in 1771)