Looking around on the GuideScroll Warframe guides I have found the following information:
GRINEER: Takes bonus damage from Armor Piercing.
CORPUS: Takes bonus damage and gets staggered by Electricity.
INFESTED: Takes bonus damage and some gets staggered by Fire, some are immune to Electricity.
Freeze damage dose 200% damage to shields where all other damge type do 100% damage.
Most enemies will recive a bonus resist based on there level that is subtracted from your damage.
Damage is listed as Normal hit/Weakpoint hit, for most that is Body/Head.
GRINEER
Everything is armored except for melee Grineer.
Normals include trooper, Lancer, etc.
Heavy include Bombadier and Gunner.
Shield Grineer takes damage as Normals, but recives 2 levels less resistance.
Commander-normal is the same as Heavy but immune to electrical/fire damage, AP/freeze not tested.
Normal Armor Piercing Fire Freeze Electrical
Sawmen 100%/300% 100%/200% 100%/200% 100%/200% 100%/200%
Normals 33%/100% 150%/300% 37.5%/75% 16.5%/33% 20%/40%
Heavy 66%/200% 100%/200% 50%/100%+ 50%/100% 50%/100%
CORPUS
Crewmen are armored.
They are Staggered by Electricity.
Moa's weak point is there midsection/gun.
Normal Armor Piercing Fire Freeze Electrical
Crewmen 81%/0% 100%/2000% 33%/100% 75%/200% 160%/400%
Moa 100%/200% 50%/100% 50%/100% 50%/100% 200%/400%
Osprey 100% 100% 100% 100% 200%
Cameras 100% 100% 100% 100% 200%
INFESTED
Normals include Chargers, Leapers, Runners, etc.
Ancient heads/bodies and Crawler bodies are armored.
Normals and Ancients are Staggered by Fire.
Crawlers have 3 areas of damage Body/Legs and Arms/Head.
Ancients have 3 areas of damage Body/Head/Lower legs and Arms.
Normal Armor Piercing Fire Freeze Electrical
Normals 100%/200% 50%/100% 200%/400% 100%/200% 50%/100%
Nauseous Crawler 66%/100%/200% 50%/50%/100% 125%/200%/400% 50%/100%/200% 50%/50%/100%
Crawler 50%/100%/200% 50%/50%/100% 100%/200%/400% 50%/100%/200% 50%/50%/100%
Ancients 25%/75%/100% 100%/200%/100% 37.5%/75%/200% 25%/50%/100% 0%
Channeling Efficiency reduces the cost per hit while channeling (holding left mouse button while having the sword equipped).
Base cost is 5 energy per hit (misses do not use energy), minimum energy cost is set to 1 Energy per strike, so even if you should get 100% channelig Efficiency, you can't get below that cap.
Also not that you can gain a damage multiplier while chanelling - ever 5 consecutive hits earns you a damage multiplier of 0.5 (I don't know if there is a cap).
Source: Warframe Wikia
Warframe forum
Best Answer
The Warframe wiki would suggest that completing a bonus objective will net you an additional 500 affinity. These bonus objectives appear to be assigned randomly at the beginning of a mission.