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Periodic Destruction
Defeat all of the creations of Mardivas's Laboratory in Nazjatar.
Periodic Destruction requires you to defeat all elemental creations at Mardivas's Laboratory in Nazjatar, unlocked after completing Legacy of the Mad Mage, and takes a minimum of 13 weekly resets to complete.
Complete Legacy of the Mad Mage
Before you can access the Laboratory of Mardivas, complete the Legacy of the Mad Mage quest chain. This unlocks the weekly quest The Laboratory of Mardivas and grants access to the cave entrance at 60.31, 30.52 in Nazjatar.
Locate Mardivas's Laboratory
Travel to the eastern end of Azsh'ari Terrace in Nazjatar and enter the cave at 60.66, 31.6. Take the road north into Azsh'ari Terrace and when the road forks, go straight and jump down off the cliff to reach the entrance.
Collect Arcane Reagents Weekly
Kill mobs throughout Nazjatar to collect three reagent types: 
Strange Volcanic Rock (Fire), 
Strange Mineralized Water (Water), and 
Strange Oceanic Sediment (Sand). Benthic items with the Elemental Instincts effect grant an increased chance of looting these reagents.
Understand the Crystal Combinations
Inside the laboratory there are 6 crystals: 3 lesser and 3 greater Arcanocrystals. For each summoning, you may add a reagent to 1 lesser crystal alone, or to 1 lesser and 1 greater crystal together, before activating the Elemental Essence Amalgamator. The following 13 combinations each summon a unique elemental: activating the Amalgamator with no reagents summons an Arcane Amalgamation; adding Strange Mineralized Water to a lesser crystal summons a Watery Amalgamation; adding Strange Volcanic Rock to a lesser crystal summons a Pyroclasmic elemental; adding Strange Oceanic Sediment to a lesser crystal summons a Lithic elemental — and each reagent type can also be combined with a greater crystal for additional unique summons.
Summon One Elemental Per Week
Each week, activate the Elemental Essence Amalgamator to summon and defeat one elemental. The Amalgamator locks out until the weekly server reset after each use. You can check whether you have completed it this week by pasting /script print(IsQuestFlaggedCompleted(55121)) into your chat — 'true' means completed, 'false' means it is still available.
Defeat All 13 Elemental Creations
Defeat every unique elemental creation across 13 weekly resets to complete Periodic Destruction. Each elemental drops approximately 2–
3 Prismatic Manapearl, and the weekly quest turn-in grants an additional 10 Prismatic Manapearl. Possible drops include 
Scroll of Violent Tides, 
Glaive of Swells, 
Slicer of Omus, 
Technique: Glyph of Steaming Fury, 
Azerite-Infused Crystal Flayer, 
Mardivas's Universally Lauded Tote, and 
Mardivas's Magnificent Desalinating Pouch.
Tips
This achievement is part of the meta-achievement Undersea Usurper, so each elemental defeated contributes toward both goals simultaneously.
At 79, 27 inside the laboratory there is an Arcane Chest — the first interaction that begins the initial investigation quest does NOT count toward the weekly lockout, so the weekly quest will appear at the book near the entrance afterward.
The weekly lockout resets with the server weekly reset, so plan to visit the laboratory each reset to progress through all 13 summons as efficiently as possible.