Let's settle this.brightness_7

Yes and No. They aren't as strong as say, the wither or the ender dragon, but they are still stronger than most normal enemies.
Also several spawn in a single monument, and in order to get the main reward for fighting them you must defeat all three (the main reward being the ocean monument itself and everything in it)

I would definitely that they are worthy of being mini-bosses though, since fights against them can be tough, and if you want to fight them you must go to a certain location (the ocean monument), and a large reward is given if you take out all three

Elder Guardian is more like a Boss

The
Elder Guardan should have a boss bar. The Elder Guardian is one of the 3
bosses in Minecraft, but it doesn't have a boss bar for some reason.
There should also be an achievement for defeating it (Like The End or
The Beginning). When you defeat the elder guardian you should get a
guardian laser that can shoot a laser at mobs or other players, it could
use a lever to turn on or off to let other players in.

Mojang considers it a boss as it was added to PE as part of the "Boss Update" (thats the only source where it was referred to as a boss)
Promotional poster for boss update

Yes