Without having to look very far, there are so many incredible beaches in Shetland. Here's a list of a few of the more 'out of the way' beaches.
The beach connecting Fethaland to the isle of Fethaland contains the ruins of an old fishing station. It's a great walk to get here and there's often lot of seals in the bay to watch.
Lang Ayre, Northmavine
Lang Ayre is a expansive red beach located on the western side of Ronas Hill. It is accessed by walking over Ronas Hill to almost the southern end of the beach. Where the stream drops down on to the beach there is a rope which can aid access. It is quite steep and gravelly however.
Located near Tresta, Sandsound is a nice small rocky beach. Usually very sheltered.
A small tombolo beach which connects the isle of Uyea to the mainland. It can be accessed along the track from North Roe but a much more interesting walk is along the coast from Sand. It's not very easy to access this beach, you have to climb down a steep rocky section. I would not advise it unless you are confident. Also, be sure to check the tide times before you set off. The beach will disappear as the tide rises.
This beach is accessed through the fields from the car park at the end of the Hannigarth road, in south-east Unst. There are also ruins of an old settlement nearby.
Little Ayre, Muckle Roe
Still very accessible but generally a quiet beach. It's located at the end of the Muckle Roe road and through a couple of fields.
Norwick Beach, Unst
Not exactly a hidden beach, it's very close to the road. But still a nice big beach in the north-east of Unst.
Sand Beach, Westside
Again, it's not very hidden but I think it's often forgotten and it's rarely busy. Be sure to visit the Sand gardens whilst in the area. There are also the ruins of St Mary's chapel in the graveyard next to the beach.