Quick guide here for the event achievements.
For the ‘Use Ability X times’ challenges:
Here is an easy nearly all hands off approach: Toolshed, MuscleWizard, and Pika all have abilities they will cast idly - Toolshed 5* ability, Pika 5* ability, and MuscleWizard 4* ability. Just load up anything, have them hold position, leave your phone on for a while, come back and they’ll have tons of progress towards the events. Recommended to do this in a Sugar High party with Windsummers for his 3* Cast Speed ability.
After that you can send in Jaina with a few healers into Clone Tower - at some point you’ll encounter a floor that will end up in somewhat of a stalemate and you can farm the rest of your event progress that way.
Or an alternate method for Jaina, send her into a Daily Dungeon with a healer as the Leader. Run through the DD until you reach an area with Tombstones… position yourself to spawn them and aggro them via the Healer casting (not Jaina), and Jaina will clean them up as they get in range.
If you don’t have the higher abilities (due to not being at the appropriate star level), then the simplest approach is probably to just load up a Daily Dungeon team with all 4 heroes: Toolshed, MuscleWizard, Pika, MoreProudJaina, and then a random Healer or Tank (depending on your power level). Let them run as far as they can go, and rinse and repeat.
For the ‘Kill guy X times’ challenges:
The Daily Dungeon is the BEST with no cost to get your kills . I highly recommend this route, so you save your energy for the things you really want to spend it on.
However if you want to do it via the Normal/Hard levels instead of grinding Daily Dungeon, and you have tons of energy to burn … here is the info you will want for where to farm efficiently.
Overjoyous Orcs!
= Overall: I would farm World 1-3 on Normal (341 Total Energy needed). Normal costs 5 energy, and you can get 22 kills, for an efficiency of 4.4 kills per energy. Hard costs 15 energy, and you can get 30 kills, for an efficiency of 2.0 kills per energy.
= Normal: World 1-3 is the best for farming
= Normal: 1-1 has 21, 1-2 has 9, 1-3 has 22, 1-4 has 21
= Hard: World 1-4 or 1-6 is the best for farming
= Hard: 1-3 has 21, 1-4 has 30, 1-5 has 22, 1-6 has 30
Greet the Goblins!
= Overall: I would farm World 3-4 on Normal (435 Total Energy needed). Normal costs 8 energy, and you can get 23 kills, for an efficiency of 2.875 kills per energy. Hard costs 18 energy, and you can get 23 kills, for an efficiency of 1.278 kills per energy.
= Normal: World 3-4 is the best for farming
= Normal: 3-1 has 13, 3-2 has 19, 3-3 has 15, 3-4 has 23, 3-5 has 13, 3-6 has 20
= Hard: World 3-4 is the best for faming
= Hard: 3-1 has 13, 3-2 has 19, 3-3 has 15, 3-4 has 23, 3-5 has 11, 3-6 has 22
Share with the Snow Legion!
= Overall: We do not have a Hard World 6 yet, so your only option is Normal; therefore I would farm World 6-7 on Normal (667 Total Energy needed). Normal costs 14 energy, and you can get 21 kills, for an efficiency of 1.5 kills per energy.
= Normal: World 6-7 is the best for farming
= Normal: 6-7 has 21, 6-8 has 19, 6-9 has 17, 6-10 has 10, 6-11 has 4, 6-12 has 15
If you go the dungeon route, you can do it all for: 1443 Total Energy. This is why most people will do it via Daily Dungeons 
Special thanks to Friendlydude5FanClub for the assist in collecting this data for everyone!
Special thanks to Psycho Romeo for sharing ideas on how to quickly complete the skill challenges!