Ash: just spam Shuriken, with the Seeking Shuriken augment
Atlas: can't think of any way he can quickly clear large AOEs
Banshee: Sound Quake. With the Resonating Quake augment.
Baruuk: unless he had a way to group or clump enemies together, his Serene Storm won't be as effective. Also, it requires him to have his Restraint eroded first.
Chroma: Effigy + Spectral Scream is the only option I'm aware of.
Ember: she'd be the easiest, because of Fireblast + Inferno. However, IIRC Nilbog has some contingencies against fire, so... *le shrug*
Equinox: Day Form. Maim. EZPZ. Even at low ability strength/high to max range, she'll still get the job done.
Excalibur: Exalted Blade, with the Chromatic Blade augment. Go blender.
Frost: either (a) go for max range and high ability strength, then cast Snow Globe and somehow pull enemies inside it before proccing Viral then smack em around, or (b) build for Avalanche spam
Gara: laziest method I'm aware of would be to go for max range and ability strength, then cast her Mass Vitrify. Allow glass to leach a bit of extra health (say, four seconds), then shatter with her 1. This should deal with any unit outside of the glass wall.
Garuda: similar build to Saryn. It would be a good idea to catch at least one enemy unit with Dread Mirror for some damage mitigation, from at least one direction. Charge Seeking Talons to max, deploy, watch the carnage as any and all enemies caught begin to bleed out.
Gauss: three words: Thermal. Sunder. Build.
Grendel: he faces the same issues as Baruuk.
Harrow: . . . Naaaah, the guy's kit doesn't seem to lend well to radial AOEs. Maybe for linear ones.
Hildryn: the newb combo should be enough: Pillage, then Aegis Storm.
Hydroid: max range, high duration hentai swarm -- I mean, Tentacle Swarm. Maybe cast Undertow before the tentacles. Maybe.
Inaros: lazy method: cast Sandstorm.
Ivara: like Harrow, she doesn't really work with radial AOE clearing. Sadly.
Khora: max range, high duration Strangledome. And possibly hit Entangle on any mook that gets dragged into the dome, letting it snag more outliers in the process. Then whack the dome repeatedly with her Whipclaw.
Limbo: max range, high duration. Cast Cataclysm then Stasis (cast order at player's discretion). Detonate when desired, or just let it run out on its own.
Loki: max range, hit Radial Disarm with Irradiating Disarm augment. Go stealth. Troll Nilbog.
Mag: high/max range, decent duration. Equip Lanka (or Zenith; mod for raw damage/crit, both weapons don't need punch through mods). Cast Magnetize, fire into bubble, watch as victims become sieves.
Mesa: Peacemaker. Nuff said.
Mirage: get a Kuva Ogris or Kuva Bramma. Mod for high duration and ability strength. Get the Hall of Malevolence augment. Cast her Hall of Mirrors. Go to town on Nilbog's arse.
Nekros: . . . Can't think how his kit could be adapted for nuking, sorry...
Nezha: his first two skills (Firewalker and Burning Chakram) might be ill suited against Nilbog, which leaves his Divine Spears. Probably mod for max range and high ability strength.
Nidus: . . . Do I still need to?
Nova: Speedva setup. Cast Molecular Prime. Get some range upwards (probably via Wormhole), fire Antimatter Drop (with Antimatter Absorb augment) downward. Aim glide and watch the fireworks.
Nyx: newb combo, Chaos + Absorb should work just fine.
Oberon: Hallowed Ground + Reckoning should do the trick. High ability strength and range (at least 240 for a full circle).
Octavia: laziest combo ever: mod for high duration and range. Cast Mallet. Cast Metronome. Cast AMP. Spam Ctrl until stealthed. Watch.
Protea: mod for max duration, high range, decent ability strength. Cast Blaze Artillery, maybe a few Shrapnel Vortexes if needed.
Revenant: Mesmer Skin. Danse Macabre. Nuff said.
Rhino: . . . Must I?
Saryn: already given as an example
Titania: her kit doesn't have any AOE nuke possible abilities, AFAIK...
Trinity: her only nuke possible ability that I'm aware of would be her Link, plus the Abating Link augment; however, near as I can remember, it's capped at a max of three enemies per cast... I might be wrong though.
Valkyr: Paralysis (plus the Prolonged Paralysis augment) is the only AOE damage skill that Valkyr has, AFAIK...
Vauban: there's several options open. Flechette Orb? Tether Coil? Tesla Nervos? Bastille? Your call.
Volt: Discharge spam. EZPZ.
Wisp: Breach Surge or Sol Gate, either option works.
Wukong: Defy. Nuff said.
Xaku: haven't gotten him yet so IDK.
Zephyr: Tornadoes.