Attack on Titan 2

Credits : GameFaqs

You have 3 ways to increase the relation between your character (the protagonist) and the AOT characters:

1. Talking to them while they have a heart above their head. You will be given a multiple choice question to test your knowledge of how to talk to the character. If you want, you can save your game before you talk to them and load your save state if you answer incorrectly. When the correct answer is selected you can see a glowing green thing.
2. Playing with one of the AOT characters in other modes (not the history mode)
3. Inviting one of the AOT character in scout missions (talk to a character and use to invite, + one of to use friend ability)
4. Using AOT characters in history mission ( + one of to use friend ability)
5. Giving gifts

Gifts

The first 2 items will increase much more your friendship level.

- Eren
Anti-Titan Manual Part 2, Perfect Replica Blades, Thick Parka, Training Equipment, Where Mom Lives, Titan Training Dummy, Anti-Titan Manual Part 1

- Mikasa
Training Equipment, Anti-Titan Manual Part 2, Perfect Replica Blade, Titan Training Dummy, Anti Titan Manual Part 1, Weapons Engineering Lecture, Emergency Kit, Rose Bouquet, Elegant Bedding, Leather Gloves

- Armin
History of the Walls, Interior Sightseeing Map, Chess Set, Weapons Engineering Lecture, Thick Parka, Emergency Kit, Quill Pen, Sketch Book, Elegant Bedding

- Reiner
Solider's Handbook, Leather Gloves, Titan Doll, Anti-Titan Manual Parts 1-2, Interior Sightseeing Map, Pomade, Elegant Bedding, Silver Ring, Golden Necklace, Thick Parka, Titan Training Dummy, Training Equipment, Special Newspaper, Regiment Metal

- Bertholdt
Elegant Bedding, Titan Doll, Anti-Titan Manual Parts 1-2, Solider's Handbook, Interior Sightseeing Map, Hungry Titan, Strange Vase, Strange Painting, Dust Rag, Ultimate Dust Rag, gold Bar, Titan Training Dummy, Training Equipment, Regiment Metal, Strange Fossil

- Annie
Thick Parka, Leather Gloves, Training Equipment, Titan Doll, Black Tea, Anti-Titan Manual Parts 1-2, Where Mom Lives, Gold Bar, Rose Bouquet, Silver Ring,Titan Training Dummy, Perfect Replica Blade

- Jean
Where Mom Lives, Weapons Engineering Lecture, Interior Sightseeing Map, Hungry Titan, Pomade, Gold Bar, Chess Set, Silver Ring, Golden Necklace, Thick Parka, Leather Gloves, Perfect Replica Blades

- Conny
Where Mom Lives, Hungry Titan, Anti-Titan Manual Parts 1-2, Interior Sightseeing Map, Gold Bars, Elegant Bedding, Thick Parka, Perfect Replica Blades

- Sasha
Marbled Meat, Dried Meat, Hunter's Armory, Field Provisions, Stale Bread, Black Tea, Anti-Titan Manual Parts 1-2, Interior Sightseeing Map, Hungry Titan, Where Mom Lives, Elegant Bedding, Thick Parka, Emergency Kit, Perfect Replica Blades, Regiment Metal

- Christa
Emergency Kit, Rose Bouquet, Stale Bread, Black Tea, Anti-Titan Manual Parts 1-2, History of the Walls, Interior Sightseeing Map, Where Mom Lives, Quill Pen, Sketchbook, Silver Ring, Special Newspaper

- Ymir
Gold Bar, Titan Doll, Black Tea, Interior Sightseeing Map, Hungry Titan, Silver Ring, Golden Necklace, Gem Stone, Leather Gloves, Special Newspaper

- Levi
Ultimate Dust Rag, Silver Ring, Perfect Replica Blade, High Quality Tea, Black Tea, Cheap Alcohol, Anti-Titan Manual Parts 1-2, Dust Rag, Training Dummy, Training Equipment, Leather Gloves, Special Newspaper

- Hange
Strange Fossil, Titan Doll, Sketch Book, Quill Pen, Weapons Engineering Lecture, Anti-Titan Manual Parts 1-2, History of the Walls, Hungry Titan, Where Mom Lives, Elegant Bedding, Chess Set, Emergency Equipment, Perfect Replica Blade, Special Newspaper

- Erwin
Perfect Replica Blade, Anti-Titan Manual Parts 1-2, Solider's Handbook, History of the Walls, Weapons Lecture, Quill Pen, Chess Set, Pomade, Silver Ring, Leather Gloves, Titan Training Dummy, Training Equipment, Emergency Kit, Regiment Metal

- Marco
Water of the Far North, Stale Bread, Fresh Bread, Quill Pen, Rice Omelet, Sketchbook, Pomade, Gold Bar, Strange Fossil, Solider's Handbook, Elegant Bedding

- Thomas
Stale Bread, Fresh Bread, Solider's Handbook, Interior Sightseeing Map, Pomade, Gold Bar, Elegant Bedding, Thick Parka, titan Training Dummy, Training Equipment.

- Mina
Rose Bouquet, Stale Bread, Black Tea, Emergency Kit, Training Equipment, Titan Training Dummy, Thick Parka, Elegant Bedding, Gold Bar, Interior Sightseeing Map, Solider's Handbook

- Miche
Perfect Replica Blade, High Quality Tea, Black Tea, Anti-Titan Manual Parts 1-2, Solider's Handbook, Pomade, Leather Gloves, Titan Training Dummy, Training Equipment, Special Newspaper

- Ouro
Ultimate Dust Rag, Regiment Medal, Black Tea, High Quality Tea, Pricey Alcohol, Anti-Titan Manual Parts 1-2, Where Mom Lives, Dust Rag, Gold Bar, Pomade, Elegant Bedding, Golden Necklace, Titan Training Dummy, Training Equipment, Perfect Replica Blade

- Petra
Where Mom Lives, Ultimate Dust Rag, Rose Bouquet, Black Tea, Anti-Titan Manual Parts 1-2, Solider's Handbook, History of the Walls, Weapons Engineering Lecture, Interior Sightseeing Map, Quill Pen, Sketchbook, Dust Rag, Gold Bar, Elegant Bedding, Silver Ring, Titan Training Dummy, Training Equipment, Emergency Equipment, Perfect Replica Blade, Special Newspaper, Regiment Medal

- Gunther
Ultimate Dust Rag, Black Tea, Cheap Alcohol, Anti-Titan Manual Parts 1-2, Solider's Handbook, Dust Rag, Pomade, Gold Bar, Elegant Bedding, Golden Necklace, Titan Training Dummy, Training Equipment, Perfect Replica Blade, Special Newspaper, Regiment Medal

- Eld
Ultimate Dust Rag, Cheap Alcohol, Anti-Titan Manual Parts 1-2, Solider's Handbook, weapon Engineering Lecture, Quill Pen, Sketchbook, Dust Rag, Pomade, Gold Bar, Chess Set, Elegant Bedding, Silver Ring, Golden Necklace, Titan Training Dummy, Training Equipment, Perfect Replica Blade, Special Newspaper, Regiment Metal

- Moblit
Sketchbook, Pricey Alcohol, Cheap Alcohol, Where Mom Lives, Quill Pen, Pomade, Gold Bar, Elegant Bedding, Special Newspaper, Regiment Medal

- Ian
Pricey Alcohol, Cheap Alcohol, Solider's Handbook, Pomade, Gold Bar, Leather Gloves, Training Equipment, Regiment Medal

- Rico
High Quality Tea, Black Tea, Solider's Handbook, History of the Walls, Weapons Engineering Lecture, Where Mom Lives, Chess Set, Rose Bouquet, Silver Ring, Emergency Kit, Regiment Medal.

- Mitabi
Cheap Alcohol, Solider's Handbook, Pomade, Gold Bar, Leather Gloves, Training Equipment, Regiment Medal

- Nile
Solider's Handbook, Cheap Alcohol, History of the Walls, Where Mom Lives, Pomade, Chess Set, Leather Gloves, Regiment Medal

- Marlo
Solider's Handbook, Fresh Bread, Stale Bread, History of the Walls, Pomade, Chess Set, Thick Parka, Emergency Kit, Regiment Medal

- Hitch
Gold Bar, Rose Bouquet, Stale Bread, Black Tea, Interior Sightseeing Map, Hungry Titan, Where Mom Lives, Golden Necklace, Gemstone, Thick Parka

- Hannes
Pricey Alcohol, Cheap Alcohol, Weapons Engineering Lecture, Interior Sightseeing Map, Where Mom Lives, Pomade, Elegant Bedding, Golden Necklace, Training Equipment

- Pyxis
Chess Set, Pricey Alcohol, Cheap Alcohol, History of the Walls, Weapons Engineering Lecture, Interior Sightseeing Map, Strange Vase, Strange Painting, Strange Objet d'Art, Quill pen, Sketchbook, Elegant Bedding

- Keith
Titan Training Dummy, Training Equipment, Anti-Titan Manual Parts 1-2, Solider's Handbook, Leather Gloves, Perfect Replica Blade, Special Newspaper

- Kitz
Pricey Alcohol, Cheap Alcohol, Solider' s Handbook, Weapon's Engineering Lecture, Quill Pen, Sketchbook, Pomade, Elegant Bedding

- Zachary
Strange Objet d'Art, Strange Painting, Regiment Medal, Pricey Alcohol, Cheap Alcohol, Solider's Handbook, Weapon's Engineering Lecture, Strange Vase, Quill Pen, Sketchbook, Pomade, Chess Set, Elegant Bedding Special Newspaper

- Nanaba
Perfect Replica Blade, Black Tea, Cheap Alcohol, Anti-Titan Manual Parts 1-2, Solider's Handbook, History of the Walls, Weapon's Engineering Lecture, Where Mom Lives, Chess Set, Rose Bouquet, Leather Gloves, Titan Training Dummy, Training Equipment, Special Newspaper

- Gelgar
Cheap Alcohol, Pricey Alcohol, Pomade, Perfect Replica Blade, Anti-Titan Manual Parts 1-2, Hungry Titan, Where Mom Lives, Elegant Bedding, Silver Ring, Leather Gloves, Titan Training Dummy, Training Equipment, Special Newspaper

- Daz
Fresh Bread, Stale Bread, Interior Sightseeing Map, Hungry Titan, Where Mom Lives, Pomade, Gold Bar, Elegant Bedding, Emergency Kit

- Nick
Gemstone, History of the Walls, High Quality Tea, Black Tea, Where Mom Lives, Strange Vase, Strange Vase, Strange Painting, Strange Objet d'Art, Quill Pen, Sketchbook, Pomade, Gold Bar, Elegant Bedding, Silver Ring, Golden Necklace

- Merchant Boss
Golden Bar, Weird Fossil, Gemstone, Golden Necklace, Weapons Engineering Lecture, Interior Sightseeing Map, Hungry Titan, Where Mom Lives, Strange Vase, Strange Painting, Strange Objet d'Art, Quill Pen, Sketchbook, Pomade, Elegant Bedding, silver Ring, Leather Gloves

While the tips are above are great, you will most likely eventually just have to grind out rep with people regardless. Personally I found it easier to make a spreadsheet of all characters and their ranks so I knew who was what level without having to constantly open the diary and look.

The most efficient way I found to grind out rep is:

1) Pick a character you want to work on, go to them on the map and press Y to invite them out on a scout mission.

2) Activate the Intensive Cleaning Week policy for 5x WoF at the vendor in the middle of town.

3) Start up the scout mission, "First Scout Mission Beyond The Walls" and go from the starting mission 1 of 4.

4) IF the character you're levelling has 0 of the current level filled in, by the time you have done all 4 missions that make up the main scout mission, they WILL have completely filled the bar up and will increase in rank when you talk to them back in the daily life area.

This is fine on Normal, each mini mission of the scout mission takes anywhere from 30 seconds to 1 min, assuming you have decent gear. For me this was the last achi I needed so had all fully upgraded gear. The longest part of it is the loading screens in between each mission.

It's important to check on other characters when you're back in the daily life area, as there is normally 3-4 that will have convo prompts each time you get back. IF the character you're taking with you fills their bar before you finish all 4 mini missions, just quit back to base, level them up and then go back at it.

With regards to gifts, the shops DO restock if you just do scout missions and it's always worth checking every gift shop every now and then as they all restock at different rates.

Christa is a good one to get to level 5 ASAP as she gives the skill Friendship that can be equipped on your char to further increase friendship gain.