You were given bad advice...not uncommon.
First of all, chlorine is absolutely 100% effective in killing all algae, and all life, in the water. That it didn't work just means some step was missed. Also, chlorine doesn't last a long time, so I'm not sure if you added some and waited a month or added some like every few days for a month. The best place to learn about algae and chlorine use is from swimming pool sites. Ponds don't use chlorine so not much help.
Yes, if you can eliminate all sunlight the algae will die. This can take more than a week. A tarp may not block enough light, so it can take even longer. Depends on the material. And after a few weeks you take the tarp off and a few days later the algae is back. To me that makes it bad advice.
Small unimportant point just because I'm a nerd...UV actually kills algae in the same way it damages our skin. It's other wave lengths the algae use to make food.
With no fish, plants or any living thing in the pond I suggest any copper sulfate algaecide. Much less expensive than chlorine and other oxidizers and easier to use. Copper kills an algae and as the cell decomposes the copper is released to kill again. So you don't have to add more very often. But you should read up on it because you don't want the copper to be getting into your garden.
So you could use what's called chlorine shock (just a lot of chlorine) and then when clear the copper sulfate and you should be good.