AlgenKiller contains copper sulfate and monolinuron.
Copper sulfate is not a very effective algaecide, at least until you get into such high doses that other flora/fauna are at risk.
Monolinuron is an herbicide in the phenylurea family. It works by inhibiting photosynthesis, in some plants more strongly than others. In short, it's a chemical blackout. Once bound to the plant, its effects can last for weeks, even if the chemical is removed through water changes. Better off avoided in any planted tank.
Your algae looks more like hair algae to me, although I'm not 100% sure. If it's hair, growth can be stopped or slowed with reduced light, reduced phosphate (if there's a *huge* excess), and overall good conditions. Existing algae can be removed mechanically, and/or killed in-place with H2O2 or Excel spot treatments.
If it's Cladophora, then it becomes far more difficult. No improvement in tank conditions will stop or slow it, as it thrives in what would be considered a perfect planted tank. It's also resistant to H2O2 and Excel to the point where spot treatments are barely effective, and can survive long blackouts. Mechanical removal still works, but unlike hair algae, it can't be yanked out from a plant 100% intact; and may spread fragments that can pop up elsewhere.
In this case, the only acceptable option I've found is treating the algae outside the tank. Remove all affected plants to a bucket with water. Disturb the algae as little as possible to avoid spreading fragments. If this means digging up a chunk of substrate, do it.
Now you can treat with a stronger dose of chemical in the bucket. Though given clado's resistance, it can still be hard to dose with enough H2O, Excel, bleach, etc. to ensure killing it without significantly damaging the plant. So I use AlgaeFix instead. It's a very effective algae killer. The active ingredient changes the surface tension of water, affecting water and gas exchange across fine structures (like algae) until the cells rupture. Three days in the bucket with the normal dose works great on algae, including clado, with no effect on plants that I've noticed. Rinse well and return to the tank. The algae may not initially appear dead, but it will dissolve over a few days.
You may be tempted to use AlgaeFix directly in your tank, and some do. But be aware it's a gamble. It's particularly lethal to invertebrates. And can sometimes kill fish too. Fish gills are *also* fine structures, directly involved in water and gas exchange; and changing the surface tension of water certainly affects them! Many times there will be no bad effects, but other times you may lose multiple fish, with symptoms of severe respiratory distress. Should you try this, if you see even the slightest hint of these symptoms, remove the chemical through multiple large water changes *immediately*. I've also done some experiments to satisfy my own curiosity that suggest fish can adapt better if the chemical is introduced gradually, divided in 1/4 doses over 24 hours, instead of dosed all at once. Though I guarantee nothing, and generally recommend AlgaeFix for use outside the tank only.