The bramma is an explosive grineer bow that deals damage in an AOE when the arrow hits any surface as well as spawning three smaller cluster bombs on impact that do considerably less damage. The weapon is broken and still needs a nerf.

Why toxin?

Toxin is the best bramma element because it always either saves a slot or boosts the weight of an element you want to proc.
Although other elements have niche uses they will not be discussed in this build. If you don't have a toxin bramma, get a toxin bramma or find a different guide as not having tox breaks all of these builds.

The 5 core mods and arcane:

Serration/[Amalgam Serration]: Your basic damage boost that lets you stack merciless. The difference between them in terms of DPS is negligible but amalgam offers a neat boost especially to archwings in in open world areas.
[Galvanized Chamber]: Multishot, almost always a mandatory mod.
Crit mods: Crtis are strong, abuse them.
[Vigilante Supplies]: Ammo mutation is mandatory as even with merceless you only have 10 shots before having to look for ammo.
Merceless: Easiest arcane to stack, boosts your ammo capacity and arrow draw speed.

THE LAST 4 MODS ARE FACTION SPECIFIC!

Grineer build:

Last Slots:
[Hunter Munitions], [Primed Bane Of Grineer].
For endless: [Hammer Shot] and [Rime Rounds].
For lower levels: [Primed Firestorm] and [Primed Cryo Rounds].

Explanation: Grineer units are heavily armoured. The best approach to dealing with them is ignoring said armour with slash procs caused by [Hunter Munitions]. These procs then get boosted by viral. Raw damage from the primed cold mod and the AOE boost from [Primed Firestorm] helps out with hitting multiplie enemies. On higher levels hitting more enemies is less of a priority than killing the ones you do hit as bomblets won't kill most enemies.

Corpus build:

Last Slots:
[Primed Bane Of Corpus], [Infected Clip], [Malignant Force]
For endless: [Hammer Shot].
For lower levels: [Primed Firestorm]

Explanation: Corpus enemies are heavily shielded. The best approach to dealing with them is ignoring said shield with tox damage and tox procs. On higher levels hitting more enemies is less of a priority than killing the ones you do hit as bomblets won't kill most enemies.

Infested build:

Last Slots:
[Primed Bane Of Infested], [Hammer Shot], [Primed Firestorm], [Stormbringer]

Explanation: Most infested units don't have armour nor shields. Meaning they are complete pushovers to borderline any build. Their heaviest units have some armour and are vulnerable to corrosive so using corrosive on all infested is a pretty safe bet.

Corrupted build:

Last Slots:
[Hunter Munitions], [Primed Bane Of Corrupted].
For endless: [Hammer Shot], [Rime Rounds].
For lower levels: [Primed Firestorm], [Primed Cryo Rounds].

Explanation: The corrupted faction consists of multiple different defense types. Although technically you should have a viral hm corrupted build for their grineer units, a tox corrupted build for the corrupted corpus and a corro raw damage build for their infested units, realistically it's a safe bet to go for the grineer build on all of them and simply use magnetic on your primer to help you deal with shields. After all Grineer are the tankiest faction. On higher levels hitting more enemies is less of a priority than killing the ones you do hit as bomblets won't kill most enemies.

Sentients Build:

Last Slots:
[Hunter Munitions], [Hammer Shot], [Primed Cryo Rounds], [Primed Firestorm].

Explanation: As of update 30.7.2 sentients are vulnerable to status effects. As they posses armour and there are no bane mods for them a slightly modified grineer build is the optimal solution for dealing with them as they cannot adapt to the true damage of slash procs.

Notes:

The cluster bombs don't offer much in terms of damage but offer a lot in terms of status chance for applying viral/corrosive.

Even without [Primed Firestorm] bramma will stagger the hell out of you. Use a status immune warframe or [Primed Sure Footed] to not be bothered by this.

You can use the alt fire while the arrows are in the air to manually detonate them. Useful if you overshoot but too niche to be remembered in the middle of a mission.

Alternatives:

Normal Banes: If you don't have Primed banes.

Primary Dexterity: If you'd like to use a combo melee as your primary damage source and your bramma as a backup.

[Critical Delay]: The weapon does not benefit from modding for firerate but modding for negative firerate will make it feel somewhat sluggish. If you have an extrernal firerate buffs or are not bothered by the extra 0.27 seconds every shot then use critical delay.

Non-Alternatives:

[Galvanized Aptitude]: Currently does not work on bows nor weapons that deal damage in an AOE as well as most, if not all projectile weapons making it triple bugged on the bramma.

[Galvanized Scope]: Doesn't trigger on proc kills even if the initial damage came from a headshot and most of your high level kills will come from headshots. Furthermore headshots with explosive weapons are unreliable.

Not using bane mods when possible: Bane mods double dip status proc damage meaning a normal bane is a 69% damage boost and a primed bane is a 140.25% damage boost. Use them or lose a massive portion of your damage.

Normal [Firestorm]: The AOE increase is not large enough to justify it.

[Vigilante Armaments] on top of [Galvanized Chamber]: VigiArama is already bad on top of the normal multishot mod so it's borderline worthless when stacked on the galvanized version. Don't use it unless you absolutely have nothing better to use.