Tactics are classified in two different ways. Every Tactic belongs to a specific element (Fire, Ice, Electric, Toxin, Umbra, Light, and Blade.) Elements are important to keep track of, because room selections will give you an element to choose from when Tactic choices appear.
Tactics also fall into an activation classification. (Attack, Skill, Dash, Legacy, and Summon). It is important to keep track of Activation classifications for Tactics, because there are rules to the Tactics that you can obtain in a run.
Rule 1: You may only have one Tactic of each Activation type. For example, if you have Attack Lightwave, you cannot also have Attack Chain Lightning.
Rule 2: This also applies to Tactics of the same name, even if they have different activation slots. For example, you cannot have both Attack Chain Lightning and Skill Chain Lightning at the same time. For reference, you can always check the Tactics Codex. If a Tactic has multiple Tier 1 (First Row) options, that means you can only have one of them.
Rule 3: If you only have the Tier 1 Tactic in one of the five Activation slots, you might get the chance to swap it for another when choosing a new Tactic. Once you've obtained a Tier 2 Tactic, you will no longer get the chance to switch out your Tier 1 Tactic. Tactics will then appear in four different rarities, Common -> Uncommon -> Rare -> Legendary, with each rarity being an upgraded version that increases the utility of what the Tactic does, such as increasing the damage or duration. These Tactics can be upgraded to the next rarity via a Tactic Ascension found in various places.
Additionally, Tactics have three stages going from Tier 1, Tier 2, and then the Tier 3 upgrade. The Tier 2 upgrades are always a choice between different upgrades to make it unique and the Tier 3 upgrade only has one option. Once you have three Tactics in one Tactic Slot, the only way to continue to upgrade that slot is with Tactic Ascensions and Double Tactics.
Double Tactics are a combination of two Tactics from different Tactic Trees and/or Elements. These Tactics combine the attributes of the two Tactics to make a powerful one that goes in the fourth slot in your Tactic slots. These Tactics require you to plan ahead by viewing the Tactics Codex and looking at the Tactic Tree to see what Doubles are possible with that Tactic. In order to obtain a Double, you'll need to obtain the three Tactics from the main Tactic and the Tier 1 tactic from the other required Tactic. Only then will the Double appear as an option in the respective element.
When passing down Tactics via a saved Evotype, any Tier 1 Tactic will be automatically equipped when you start a new run. Tier 2, Tier 3, and Double Tactics will not be equipped until you obtain the necessary Tier 1 Tactics. Double Tactics, when being passed down, have the unique property of often only needing the base Tactic associated with it, allowing you to get a Double that only requires one Tactic Slot be filled and creating a new combination in the now open slot.
Once you've filled in the first five Tier 1 slots, you'll only see Tactics of those Tactics' respective element, allowing you to only focus on upgrades at that point. Inheriting certain elements allows you to manipulate how likely you are to see a certain element without sacrificing any Mind Crystal slots. When attempting to get the "1+1>2" achievement, this significantly helps steer your five Doubles in the right direction.