One of the biggest changes that Final Fantasy VII Remake makes to the original game is the way in which the party acquires materia. While certain types can still be purchased from shops or found scattered throughout Midgar, the majority of the materia that you'll be using comes from a scientist named Chadley. Rather than everything being available from the get-go, however, you'll unlock it gradually be completing a series of tasks and challenges.
You'll first encounter Chadley in Chapter 3 as part of the main story and will be asked to complete a Battle Intel Report to help him with his research into materia. After completing it, there'll be a further 19 reports to take care of which will gradually unlock as the game's story progresses. You'll need to hand in each one by returning to Chadley, although as he shows up in numerous locations throughout the city this shouldn't be too much of an issue. Unfortunately though, the same cannot be said about actually completing some of these reports.
Battle Intel Report 01 - Monster Bio Pt. 1
Conditions: Assess 2 Enemy Types.
New Materia: Auto-Cure Materia
Equip the Assess materia and then head over to Scrap Boulevard. You'll need to find two different types of enemy and then use the Assess command from the battle menu to scan them. Even after completing the report, you should get into the habit of assessing every new enemy type that you encounter as not only is the information useful, but there are several other battle reports that require the use of the Assess command.
Battle Intel Report 02 - Magic Elements Pt. 1
Conditions: Hit enemies vulnerable to fire, ice, or lightning using the appropriate magic (Number of attacks: 1 for each element).
New Materia: Wind Materia
By assessing enemies, you'll be able to find out if they have any elemental weaknesses. To complete this report, all you'll need to do is find enemies that are weak to Fire, Ice and Lightning attacks and hit one of each using the appropriate element.
Battle Intel Report 03 - The Stagger Effect Pt. 1
Conditions: Use unique abilities on staggered enemies and charge the ATB gauge 10 times.
New Materia: First Strike Materia
In order to stagger an enemy, you'll need to completely fill the orange bar that's beneath its name. The easiest way to do this is by using Tifa's abilities, although spells and other special attacks will do the job as well. Once staggered, just be sure to mix up which abilities you're using and you should complete the report in no time.
Battle Intel Report 04 - The Stagger Effect Pt. 2
Conditions: Stagger 15 enemy types.
New Materia: ATB Boost Materia
You shouldn't really have to go out of your way to complete this report, so just keep playing through the game until you've reached 15. If you want to speed things up a little, be sure to use abilities and spells during combat rather than just regular attacks. Also, remember that if an enemy is Pressured, its stagger gauge will fill much faster.
Battle Intel Report 05 - Combat Simulation: Shiva
Conditions: Defeat Shiva.
New Materia: Shiva Materia
Shiva is the first of four summons that can be unlocked through defeating them in the Combat Simulator. She shouldn't prove too much of a challenge, but be sure to back off when she begins casting one of her big attacks and hit her with Fire attacks as much and as often as possible. If you're really struggling, try pairing an orb of Elemental materia together with an orb of Ice materia in your primary attacker's armor to drastically reduce the damage that they take.
Battle Intel Report 06 - Monster Bio Pt. 2
Conditions: Assess 10 enemy types.
New Materia: Steadfast Block Materia
If you've been assessing every new enemy type that you encounter as recommended above, you should have already met the criteria even before this report is unlocked. If not, re-equip that Assess materia and assess some new enemy types. This isn't the last Monster Bio report either, so keep it equipped and keep assessing new foes to make the next one a lot easier.
Battle Intel Report 07 - Magic Elements Pt. 2
Conditions: Exploit weaknesses of 15 enemy types.
New Materia: Steal Materia
This is another report that you'll be working towards naturally and will likely be marked as complete the moment that it's unlocked. If not, keep an eye out for enemies with elemental weaknesses and hit them with the appropriate spells until you've reached the required number of enemy types.
Battle Intel Report 08 - The Manipulation Technique
Conditions: Defeat 2 or more enemies with a single attack.
New Materia: Provoke Materia
The fastest and easiest way to complete this report is by pairing the Magnify materia with an orb of Ice, Fire, Lightning or Wind materia so that it targets all of the enemies in battle rather just one. In reality though, killing two enemies is something that you'll likely do naturally as you play; particularly if you use a lot of abilities.
Battle Intel Report 09 - Monster Variants Pt. 1
Conditions: Defeat monsters of 3 unique varieties.
New Materia: Synergy Materia
This one will unlock naturally as you make your way through the story, although you can speed things up by completing some of the many optional side quests found throughout the game. These occasionally put you up against more powerful variants of common monsters; with several showing up in the Chapter 3 side quests alone.
Battle Intel Report 10 - Combat Simulation: Fat Chocobo
Conditions: Defeat a fat chocobo.
New Materia: Fat Chocobo Materia
This is by far the easiest of the four summon-based combat simulations and shouldn't cause you any real trouble providing you keep moving around. Fat Chocobo is incredibly slow, so just get behind it as often as possible and be sure to take out any enemies that it happens to spawn in (Cloud's Triple Slash technique works great in this regard).
Battle Intel Report 11 - Monster Bio Pt. 3
Conditions: Assess 20 enemy types.
New Materia: Item Master Materia
If you haven't learnt your lesson by now, you're probably not going to. Assuming you've been remembering to assess new enemies, however, you should have already scanned the required number by the time the report unlocks. There's one final report that's tied to assessing different enemy types coming up, so keep on doing what you're doing even after this report has been completed.
Battle Intel Report 12 - The Stagger Effect Pt. 3
Conditions: Increase stagger damage bonus to 200%.
New Materia: Parry Materia
This is one of the more annoying battle reports to complete, although once you understand exactly how the stagger mechanics work, it shouldn't take you too long to achieve. The best enemy to try this against is definitely Fat Chocobo though, as its stagger period lasts a lot longer than most of the other foes in the game and its easily accessible through the Combat Simulator.
First, stagger the enemy and then hit it with abilities to raise the damage percentage as quickly as you can. You can do this by using Tifa's Chi attacks (triangle) and will get a bigger bonus by using her Unbridled Strength ability before hand. Aerith's Ray of Judgement ability is also useful here; as too are the Focused Thrust and Focused Shot abilities for Cloud and Barret respectively.
Battle Intel Report 13 - Refocus Analysis
Conditions: Trigger Refocus 2 times.
New Materia: ATB Assist Materia
This is an easy report to complete, but one that will require a fair amount of your time. You'll need to equip your newly acquired Refocus materia and then find yourself a nice, long battle (the combat simulator is probably your best bet here). Wait until your limit gauge fills up and then use Refocus. As per the conditions, you'll need to do this twice.
If you've already reached chapter 14 by this point, you can get your hands on the Transference Module and Spectral Cogwheel accessories by scoring 30,000 points in Whack-a-Box. These will allow you to fill up the limit gauge by consuming ATB charges and MP respectively and can speed up the entire process quite a bit.
Battle Intel Report 14 - The Stagger Effect Pt. 4
Conditions: Stagger 40 enemy types.
New Materia: ATB Stagger Materia
This is another one of those reports that should be done and dusted the moment it unlocks. If for whatever reason it isn't, try and adjust your play style a little to make better use of the stagger mechanics. Doing so should also make your playthrough considerably easier.
Battle Intel Report 15 - Combat Simulation: Leviathan
Conditions: Defeat Leviathan.
New Materia: Leviathan Materia
Leviathan has some fairly powerful attacks although shouldn't cause too much trouble to a well leveled party. It has a habit of flying up into the air though and so it can be useful to equip everybody with elemental spells to hit it while it's out of range. Also, try to save your summon until one of these phases as a summon's final attack will bring Leviathan back down allowing you to switch back to physical attacks.
Battle Intel Report 16 - Monster Bio Pt. 4
Conditions: Assess 30 enemy types.
New Materia: Enemy Skill Materia
This is the last of the Enemy Intel related reports, so, assuming you've been assessing enemies as you go and have already assessed enough types to complete it, you can finally remove the Assess materia from your loadout if you so desire. It's probably worth keeping it equipped if you have the a free slot though as knowing an enemy's strengths and weaknesses can be incredibly useful towards the end of the game and in Hard Mode.
Battle Intel Report 17 - Weapon Abilities
Conditions: Acquire all 16 weapon abilities.
New Materia: Skill Master Materia
Each weapon in the game has its own special ability attached to it and by using these four of five times in battle, you'll be able to master the ability so that it can be used even when the weapon is no longer equipped. You'll get a message letting you know when an ability has been mastered, but if you miss it, you can always check the proficiency meter in the Materia & Equipment menu (highlight the weapon and then look under the picture to the right of the screen). There are actually 24 weapons in the game, but you'll only need to master 16 of the abilities to complete the report.
Battle Intel Report 18 - MP Consumption
Conditions: Master all 12 types of magic materia.
New Materia: MP Absorption Materia
This is by far the most time consuming of all of the battle intel reports as it requires you to master one orb of each of the green magic materia (Barrier, Binding, Cleansing, Fire, Healing, Ice, Lightning, Poison, Revival, Subversion, Time and Wind). You should have already mastered quite a few of these by now, but will likely still have some way to go to master an orb of Revival materia due to it requiring a total of 5,000 AP.
You can speed things up a little by picking up the Pedometer materia from outside Aerith's house in Chapter 14 and then running around until it turns into the AP Up materia. Next, pair this with an orb of Revival materia in a connected materia slot and you'll cut the amount of time it takes to master it in half. You can also use the combat simulator to grind AP a little faster or continually repeat the garage section at the beginning of Chapter 16 if you've already reached that point in the story.
Battle Intel Report 19 - Monster Variants Pt. 2
Conditions: Defeat monsters of 10 unique varieties.
New Materia: HP Absorption Materia
As with the last Monster Variants report, this is something that you should unlock naturally as you work your way through the game. Again though, completing side quests can help speed things up quite a bit; especially those found in Chapter 8 and Chapter 14.
Battle Intel Report 20 - Combat Simulation: Bahamut
Conditions: Defeat Bahamut
New Materia: Bahamut Materia
As you might expect, Bahamut is the toughest of the four summon related Combat Simulations although shouldn't pose too much trouble to your party at this point in the game. Just be sure to keep everybody alive and try and time your staggers for when he begins to countdown to its powerful Megaflare attack.
Revival Earrings can also be useful here, as too can weapons with the Reprieve ability as this will allow your party members to tank some otherwise fatal hits. Bahamut has no elemental weaknesses, so it's really just a case of hitting him with everything you have and healing regularly until he's down for the count.