If you have browsed through my build suggestions, you may notice that most of my builds are hovering around level 70 and 80. These are not challenge builds that I intentionally keeping my character's level "low", rather I level up when needed and I find myself beating NG between level 70 and level 80 since my second build. (Remark: I level up freely on my first build so that I can afford to try out almost all the weapons and spells. Just part of learning process.)
These so-called level 120 limit for PvPers' are ideas carried on since Demon's Souls. In Demon's Souls and Dark Souls 1, players needed to have significant trade-off to maximize their character's ability even at level 120. However, in Dark Souls 3, as well as Bloodborne, level 70-80 would be more appropriate to beat NG, and players are required to have significant trade-off among various stats to maximize offensive and defensive abilities. At level 120, there will be no trade-off and easily overpowering in NG PvE.
Don't believe me? Try it out yourself using one of my PvE suggestions, especially, if you are willing to learn each PvE enemy's attack pattern and weakness. No summoning phantom is required.
A caster build that can cast variety of spells with effective melee as backup.
Right Hand Weapon 1: Deep Battle Axe, Hollow Estoc
Right Hand Weapon 2: Scholar's Candlestick
Left Hand Weapon 1: Pontiff Knight Shield
Left Hand Weapon 2: Sorcerer's Staff, Pyromancy Flame, Crystal Chime
Sorcerer's Set for early part of the game.
Pontiff Knight's Set when available.
Black Set by the end of the game.
Great Heavy Soul Arrows/Soul Spear/Chaos Bed Vestiges/Vow of Silence
Great Magic Weapon/Carthus Flame Arc/Crystal Magic Weapon/Dark Blade
Charcoal Pine Resin
Gold Pine Resin
Human Pine Resin
Havel's Ring/Sage's Ring
Chloranthy Ring/Witch's Ring
Scholar Ring/Bellowing Dragoncrest Ring
Priestess Ring/Ring of the Sun's First Born
Stat leveling suggestion:
1. Level up endurance to 18 first.
2. Level up dexterity to 12 for Estoc.
3. Level up vigor a little bit, if needed.
4. Level up Intelligence and Faith to 30 each.
5. Level up Attunement to 20.
6. Level up Vigor to 20 and you can easily finish first playthrough.
Since this build is focusing on spell casting with melee backup, thrusting weapon is good option. You will need to rely on Soul Arrow and two handing the Deep Battle Axe for melee until you acquire Estoc.
At such low melee stat levels, this build is a good candidate to take advantage of using hollow weapon for its added luck bonus at the cost of staying on hollow form with 30+ hollowing. In order to stack up hollowing, you must accept assistance from Yoel of Londor and allow him drawing out your power five times; simply by committing suicide about 10 times in Firelink Shrine by climbing up high and jump down or jump off cliff at ludex Gundyr bonfire. After acquiring five dark signs from Yoel, Yuria will appear and guide you through rest of the quest. She also sells you the Londor Braille Divine Tome to acquire Vow of Silence, and you just need somebody reading it for you.
Similar to a refined build for melee only character, dark build allows player to choose great variety of spells, miracles, and pyromancies. My list of spells and miracles and pyromancies are my choices, you want to choose spells, miracle, and pyromancies based on your play style and comfort level.
Another bonus of Londor hollow build is that you will have powerful NPC, namely Londor Pale Shade. Londor Pale Shade wields the Morion Blade and she is surprisingly enduring in various boss fights. If you are having problem with some bosses, where Londor Pale Shade is available, you want to summon her. If you wish to shorten those boss fights, she will be a good choice. (Remark: Some people may call it cheating summoning NPC. NPCs are part of the game, everybody should have freedom to play the game his/her way with responsibility.)
Unless you wish to forgo Irina's good ending, you won't have all dark spells, miracles, and pyromancies until late in the game. Luckily, you have great choices of other spells, miracles, and pyromancies. Like other caster builds, this is a relatively easy build.
Regarding fighting Aldrich, you want to rescue Karla at Profaned Capital and acquire Vow of Silence first, or give just Londor Braille Divine Tome to Irina to acquire Vow of Silence, as that miracle will nullify Aldrich's sorceries including her Darkmoon Longbow attacks.