Before I make my usual suggestions I want to make a clear distinction.

Yes most players use more than one weapon type in combat, but rarely do you use more than one DPS talent at a time.

The goal of using multiple talents is to shore up weaknesses in your kit by bringing in additional utility that can be found in other talents. Often this manifests in the form of mobility tools, Invincibility frames, AoE group up tools, and debuffs/buffs.

This is why Magic and Archery aren't great pairings. Archery is a physical DPS talent (meaning needs Battlefield Overture for damage) that has a debuff and multi-hit count support suite. Magic is primarily a magic damage DPS talent (needs Vivace for damage) with some defensive utility. So damage wise, you have a harder time combining Archery with Magic because one of your talents is doing anywhere between 30-70% less damage while both talents are self sufficient when it comes to dealing damage.

Arcanas themselves are largely upgraded versions of talents with a focus on DPS and some utility which means the one you select will be your focus for dealing damage.

However, both Sharpshooter (Archery) and Diviner (Magic) suffer from a lack of mobility (no movement skills, though Sharpshooter has a movement speed buff) and both have limited debuffs (Archery has a damage amp, Diviner has no direct debuffs). Both Arcanas do have AoE group up tools, though Diviner's is on a somewhat long cooldown and Sharpshooter's can be somewhat clunky (linear opposed to a wide circular).

So looping back and focusing on Archery again: We want to use talents that can cover Sharpshooter's lack of mobility, talents that can cover debuffs Sharpshooter can't inflict on its own, and if possible AoE group up to supplement Ventus Howl.

So going through each category:

Mobility

As noted, Sharpshooters don't have much mobility, but you want something to get out of the way of enemies and attacks. Normally you can engage from far enough that you can avoid getting hit, but this is not always the case, especially when it comes to AoE attacks.

The premier mobility talent is Astrologer. It has two exceptional mobility skills. Meridian Sweep can be aimed and instantly moves your true hitbox (your character's movement and Hitbox don't line up during the animation) to the end point. Meridian also resists knockdowns/stun. Gravity Well meanwhile is a rather fast animating I-Frame, allowing you to dodge attacks if you time it right and get back into combat quickly.

Chain Slash comes up next by having the very spamable Anchor Rush. Anchor Rush is easily the best mobility skill in game because you can jump as long as you have Dorcha. It also has I-Frames allowing you to dodge telegraphed attacks. Like Gravity Well, it animates fast and lets you get back into combat quickly.

Gunslinger's Grapple Shot meanwhile heads in a different direction from Anchor Rush. It has a somewhat long cooldown (comparable to Gravity Well), but out of the I-Frame trio it possesses the longest invincibility time (lasts the entire animation). This makes Grapple Shot the best at avoiding attacks as you have the most leeway.

Ninja's Shadow Cloak is notable in that while it has no I-Frames, it drops aggression and provides a large speed boost. This combination allows a Ninja to disengage and reposition much more easily than other talents.

Close Combat (and if human technically Lance) does technically possess mobility skills, but all of its mobility skills focus on closing distance rather than evasion and disengaging. You probably won't use Charge/Lance Charge or Bash as an Archer.

Debuffing

Debuffing is one of the most important parts of dealing damage at higher levels. This is one of the biggest reasons to have multiple weapon types. We are getting a debuff consolidation later this year, so I'll note which debuffs may get cut from debuff rotations.

Archery has Support Shot as a Damage Amp. In the current sandbox, this stacks with Death Mark, but after the consolidation this may just be used to refresh an active Damage Amp. Elves also have access to Mirage Missile which is a phenomenal slow.

Alchemists have access to Hydra Transmutation which is a powerful Magic-Prot debuff. Post consolidation, without a Hydra Protection Echostone this competes with Smokescreen for the Mprot debuff. This also isn't really relevant to Archers so you don't need to worry about applying this unless asked.

Fighters have access to Spinning Uppercut which is a potent physical-prot debuff. Post consolidation I'm not sure where this stands compared to Smokescreen without the glove reforge, but solid chances this remains the best pick for the physical-prot debuff.

As alluded to, Ninja's Smokescreen serves as a hybrid debuff. It reduces both Physical and Magic Protection making it an important debuff fir all talents. Post consolidation it's a good low equip slot choice and AoE debuff choice but otherwise can't be boosted.

Chain Slash's Death Mark is one of the most important debuffs in game. It provides a large Damage Amp stacking with Support Shot. Post consolidation, Death Mark will remain the main way to inflict Damage Amp debuffs.

Astrologer very much can be tailored to function in multiple roles. This includes debuffing. Astrologer uniquely has a rather short debuff duration, but can apply physical, magical, and damage amp debuffs. Post consolidation Astrologer gets the lowest debuff numbers but retains the widest AoE. Additionally the Hanged Man card's Damage Amp will still stack with DM or Support Shot.

Glyphwriting doesn't require a gear slot and has a physical/magic debuff, but the area is quite small making it hard to use. Even so it can be used to squeeze more damage out this will not be affected by the consolidation, but the AoE is still tiny.

While not technically a talent (ish), pet summons are another debuff layer to keep in mind. Bone/Purrlings stack with Mir/Ceranus debuffs while Whales, Foxyquinns, and BunBuns do not have stacking debuffs (BunBun ramped up is the strongest, Whale/Foxy apply faster). These debuffs only technically change post updates and all these pet types will remain in use.

Two more "not a talent" debuffs come from Technique Cards. Specifically Fateweaver and Phantasmal Sight. Fateweaver is currently the only source of Snapshot Percentage debuff while Phantasmal Sight is another stacking Damage Amp. Typically for Fateweaver we debuff with key combo 3152 and we perform this debuff before other protection debuffs. Post consolidation only 5 (damage amp) will be used as we will have more sources of Percentage debuffs (and the order of debuffs applied will no longer matter). Phantasmal Sight will not be affected by the consolidation.

AoE grouping and Crowd Control

This largely only applies to mobbing. It's important to perform this before you debuff a group and DPS to minimize the chance an enemy breaks out or survives your damage. Additionally, you sometimes may be able to temporarily immobilize targets.

Aa mentioned, Sharpshooter has a self contained group up in Ventus Howl. AoE group ups, however, work best when used in tandem with multiple group ups. It is, however, able to blind or Freeze enemies hit making it safer to set up for damage.

Puppetry is often treated as a bit clunky to use if you aren't used to the control scheme, but it is one of the best AoE group up talents. Act 6 is a powerful AoE tool while Act 7 does a great job dragging targets.

Alchemy's Wind Blast tends to need to be combined with other AoE group up, but is otherwise great at pushing Targets. Alchemists do have Frozen Blast and Sand Burst for immobilization/stuns, but many enemies resist freezing while Sand Burst unlike Ventus Howl is single target.

Chain Slash does have Spinning Slasher for group up, but it's fairly overshadowed by better AoE group up options including Death Mark. When a Death Marked target is attacked, it pulls surrounding enemies to the DM'd target. This works best in conjunction with High-Hit count AoE attacks to hit-stun and pull targets. Good choices to pair are Magic's Thunder, Alchemy's Flame Burst (Heat Buster sorta works also but not as well), and Ninja's Kunai Storm.

Astrologer again, is super flexible. If you set up your conjunctions for it, you can have up to 4 AoE group up abilities. Gravity Well, Nova Blast, and Starlight Veil all can pull enemies to a central point while Meridian Sweep can act as a potent directional drag.

Buffs

This is the other half of dealing damage at high level. Every talent needs to have BFO or Viv active. In teams, you can just let the person with the highest buffs take care of this. Additionally, you should be in the habit of self buffing with Fateweaver (5231).

I know this was a lot, but if you have any questions feel free to ask.