This only tracks for non-DLC stages.
This can be tracked via the the Level select Screen in the Tavern. To make it count you must complete the level either by letting the crystal get destroyed or beat the final wave.
To unlock Pure Strategy for any given level at Medium, you must play that level normally on Medium or harder.
Pure Strategy is unique in your characters can not attack, or build/summon or repair during the battle phase. However the mobs won't attack your character. Also Mobs will not be elemental, so you can use most towers without worrying about some being immune to them. Only certain enemy types will appear, so you don't need worry about Sharks, Djinn or Ogres.
It's strongly recommended that you use Builder spec characters for this mode, and that are higher level a possible. Only Passive effects of some pets will apply, and best to boost defence stats.
Out of the "Classic" Characters, The Squire and The Apprentice towers are recommended, as these provide damage that won't result in "damaged" Defences. The Monk's Aura and the Huntress Traps are generally recommended as a back up for the other defences that have failed, if they're used at all.
From DLC Characters: The Series EV Buff beam works wonders with the range towers. The Summoner's Minions can be used to add extra towers in exchange for Mana, as the Archer and Mage Minions can used for extra damage and provide much needed heal during combat phase. When a Minion stands on Buff beam it gets boosted like other towers.
As a builder, you should have already experienced the map have an idea on where the Choke points are.
Unlike the rest of the game, adding more players won't add to the Mob count. It does effectively allows the builder to hold more Mana or cover more areas.
As you can upgrade during combat, It's recommended that you upgrade Ranged defences first, then the wall as they get damaged. Upgrades not only boost the stats of a Defence, it will repair it if damaged.
In later stages, you may want to consider rebuilding walls to allow you to perform upgrade "repairs" during combat.
As you need to let the level "complete," It's recommend that you continue beyond the required Wave 10, to earn pets for getting to Wave 15 and Wave 25, which are required for other achievements and boosting your stats for later Stages.