If you were to use the artifact, it will deal damage to it & its life will decrease over time for 30 seconds I think, so be quick to killing it. Other than that, it will be easier for your air units to take it out
Cloaked wraiths are awesome against it provided it can't see you via an overseer (the morphed form of an overlord) or other detector, Least thats what i did when i did the map, mind you it was on casual diffuculty. so it might not be so easy.
On normal I hit it with a group of vikings, I believed around 16-20 of em. Fully upgraded of course. As for Kerrigan, since she can just 1 shot a cruiser, logic says throw the cheapest thing, Marines. Get a lil Marine and Medic ball, adrenaline rush and go to town.
On Normal mode, I had about 10 Battlecruisers and a few (4-6) Vikings with Viking mercs. I used the Artifact to clear out everything because Kerrigan is also in battle. Cleared her out first with a 4 Yamatos and siege tanks. I let my built Turrets take damage from Levi and Vikings shoot from a distance. 6 Yamatos then finish off with everything. Managed to kill the Levi and Kerrigan with lots to spare 'til the timer ran out.
You can try to drag Leviathan towards your base with some flying units.Have him occupied with Missile Turrets and use a combination of Marines and Goliaths on the ground-make sure it's close enough so they can hit it and Vikings and Battlecruisers(Jackson's Revenge will come pretty handy) in the air.
For Kerrigan,if you can deploy at least some Thors go for it.When you do their special attack(250 mm Cannons),Kerrigan will be stunned.
Just train a lot of vikings through out the corse of the level and you should be able to beat him and have enough left to hold off kerrigan. Also dont build any more battle cruisers, they take to much time to build. It worked for me any way.
All you have to do is kill the leviathon with air like you said and hit kerrigan with mass marines/medics. She has nothing against them. Don't waste expensive units like thors/battlecruisers. Kerrigan will justs use her 1 shot attack and it isn't worth it.
for the Leviathan, mass vikings. He can only attack a certain number of them at a time and some of those attacks will get through. 16 should do him in with 12 or so surviving as long as their tech level is decent.
For Kerrigan, she has an insta-kill attack that she uses once. Send in a lone marine decoy then slam her with everything else hard (except siege tanks. those dont work on her, though you can undeploy them for better damage). You can also use decoy bunkers to force her to psi-wave a useless bunker instead of the ones that are actually hurting her.
For the Leviathan I used about 20-30 Vikings in Aerial Mode, both upgrades purchased, all the mercenaries Vikings as well, and ship weapons and armor fully researched. For a final touch I told 6-9 science vessels to Move with one of the mercs as the goto place. That way they went (at a slower pace) wherever the Vikings did and started healing any damage incurred. Or, as Swiftelf mentioned, use a bunch of cloaked Wraiths. Or if you're feeling really crazy have a few cloaked ghosts/specters nuke the spot the Leviathan is at and use flyers to keep him there or have the flyers lure him into the blast radius after initiating it. Doing it from the bluff the artifact is on is a good way to hit Kerrigan as long as you don't aim too far and she doesn't kill the guy guiding the nuke.
Kerrigan can try putting a bunch of Perdition turrets in front of the bunkers with a bunch of tanks in siege mode on the bluff. Don't put Siege Breakers close to the edge or it'll be the one lifted up and killed. Or have about 6 or so Battlecruisers by the artifact, select them all, push Yamato gun, and then hold shift while you target her as many times as you have cruisers. They'll go together and blast her for a decent amount of damage, just be careful they're not doing anything else like attacking another target or they'll kill the target first before using the cannon. Put a row of overlapping Zerg towers so if one is destroyed another can take its place. If it's the Control Tower than that means more Zerg units under your control. If it's the Slow Tower it'll slow the Zerg down, even if they destroy a tower, and make it easier for your defenses to take them out. As a last ditch effort try to save the artifact's Nova Blast until she's close by as it does a fair amount of damage to her (will still have to pound her though).
What I did was I made Vikings merc, a Thor and artifact nove blast just use the nova blast, disract the leviathan with the Thor than have your Vikings and if you want battle cruisers to kill the leviathan