Biggest Asteroid i've seen 137,290 Concentrated Veldspar.
Enemies ------- Hardener to use --------- Dmg type to use

Blood Raider --- EM/Thermal --------------- EM
Guristas ------- Kinetic/Thermal ------------ Kinetic
Sanshas ------- EM/Thermal --------------- EM
Serpentis ------ Thermal/Kinetic ------------ Kinetic
Angel. --------- All Resis (pri. Expl. ,Kin.) --- Explosive
Mordus -------- Kinetic/Thermal ------------ Kinetic
Rogue Drones -- All Resis (pri. Expl. kin) ---- EM
Mercenary ----- All Resis (pri. EM, Therm) -- Thermal
Minmatar. ------ All Resis ----------------- Thermal (Explo)
Gallente. ------- Kinetic/Thermal (sec..EM) --- Thermal
Amarr --------- EM/Thermal. -------------- Thermal
Caldari -------- Kinetic/Thermal ------------ Kinetic
The Seven ----- All Resis ----------------- Thermal
You ----------- Whatever ---------------- Any

Targeting systems

Caldari - Gravimetric
Gallente - Magnetometric
Amarr - Radar
Minmatar - Lada