>>19049820A 252 Atk Garchomp can not kill a 252 HP/0 Def Aegislash-Shield, even with Stealth rock damage (Garchomp's damage with EQ peaks on slash at around 83%).
208+ SpA Aegislash-Blade Hidden Power Ice vs. 4 HP / 0 SpD Garchomp: 360-424 (100.5 - 118.4%)
So a specially oriented Aegislash just using physical for coverage can kill the chomp without rocks.
100+ SpA Aegislash-Blade Hidden Power Ice vs. 4 HP / 0 SpD Garchomp: 336-396 (93.8 - 110.6%) -- guaranteed OHKO after Stealth Rock
He'll be able to spread stats a bit more evenly between attack and defense with rocks as well.
100+ SpA Aegislash-Blade Hidden Power Ice vs. 4 HP / 0 SpD Dragonite: 292-344 (90.1 - 106.1%) -- guaranteed OHKO after Stealth Rock
It won't be able to kill if multiscale is still intact, though.
100+ SpA Aegislash-Blade Hidden Power Ice vs. 252 HP / 0 SpD Gliscor: 368-436 (103.9 - 123.1%) -- guaranteed OHKO
100+ SpA Aegislash-Blade Hidden Power Ice vs. 252 HP / 4 SpD Landorus-T: 348-412 (91 - 107.8%) -- guaranteed OHKO after Stealth Rock
Defensively:
0 Atk Gliscor Earthquake vs. 252 HP / 0 Def Aegislash-Shield: 146-174 (45 - 53.7%) -- 34% chance to 2HKO
252+ Atk Dragonite Earthquake vs. 252 HP / 0 Def Aegislash-Shield: 172-204 (53 - 62.9%) -- guaranteed 2HKO
252+ Atk Landorus-T Earthquake vs. 252 HP / 0 Def Aegislash-Shield: 272-324 (83.9 - 100%) -- 6.3% chance to OHKO
Aegislash with HP Ice can handle all of them decently enough with rock support.