Rolls for Days

You can't really replace Arjuna with Archer of Shinjuku because they have different role.

Honestly Avenger of Shinjuku isn't that amazing of a unit gameplay wise. While they do have higher base stats for a 4 star their skills are very mediocre due to their short duration and lack of any real crit performance up. Avenger class advantage isn't something that is often needed and you can always get them in another roll on a different banner.

As far as leveling up another archer, know that Arjuna is an AoE servant and that Archer of Shinjuku is a ST and they can't really be compared as they have different use cases. Archer of Shinjuku is not the strongest archer in the game, and seeing as you have Artoria Archer already you should be set on that front already provided you can support she needs. I would highly recommend looking at what servants you want that come out in the future so you can save mats and QP for them.

Doggo is still one of the best Avenger out there, he's worth the shot.

Reminder, Avenger list :
- Jalter - 5* ST Buster Avenger. Boss slayer, Crit damage dealer.
- Angra Mainyu - 0 * Quick Avenger. Damage returner, Crit damage dealer.
- Gorgon - 4 * AOE Buster Avenger. Farmer, Burst damager and disabler.
- Doggo - 4 * ST Quick Avenger. Boss slayer, Crit damage dealer, sustained DPS.
- Edmond Dantes - 5* AOE Quick Avenger. Farmer and Wave clearer.

Doggo is the best 4 * ST Avenger for now, and the dog having no competitor. His kit is also good for harder contents, for example : he can remove your enemy buffs, reduce your damage taken up to 70 % by using his skill alone, Crit star absorbtion, increase his own Atk by 30 % for 2 turns and his NP also has sure hit, which is nice.
You can divide the def up and damage reduce buff, for example the first turn you use 40% def Up and the next turn you use 30 % atk down and you can use another damage reduce skill from your support to further increase your team staying power. He's so good for harder content and challenge.
Avenger 1.1 atk modifier + doggo high base atk + 30 % self atk up with short CD, it's good.

I got a copy of doggo and it's good to have a loyal dog in my Arsenal.