Doomsday is required in all matches of challenge battle 5. There are three possible characters you could choose: Doomsday/Regime, Doomsday/Prime and Doomsday/Containment. While Regime Doomsday is given by the Starter Pack, he is a silver card and thus has much lower stats and he has a poor passive. Prime Doomsday is a strong card, and he is always available for purchase (while Containment Doomsday can only be found rarely in Challenge Booster Packs and the Most Wanted Pack, if you haven't unlocked him from his challenge over a year ago; it is not practical to try and get him solely for this challenge), so he is the best to go for if you don't have a good Doomsday card already.
If you are forced to use a Doomsday card much weaker than your top cards, remember that block gear remains extremely efficient at low stats.
While some players may find challenge battle 1 (bronze only) and 3 (silver) to be harder due to the lack of strong bronze or silver cards, challenge battle 5 is generally seen as the hardest with one exception: Raven/Prime. The power of her passive at any level cannot be overstated and will make nightmare challenge battle 5 much, much easier for any player.
A warm-up "gimmick" level, in a manner of speaking. Darkseid's passive gives Nightwing and The Flash a lot of damage and health, but they are still nowhere near as good as gold cards.
Challenge: Power Surge!
Arkham Origins starts with 2 bars, but he is capped at two and neither of his teammates could change that. Without Harley Quinn/Arkham, just block his Winged Avenger at the beginning and call it a day. If you are a less equipped player, you can try to use a basic combo on him at the very beginning of the match to knock him back and then block, which has a high chance of causing him to use his weak Explosive Batarangs at a range instead.
This team can be annoying, as Krypto Lex Luthor gives a large health boost, both him and New 52 Nightwing has an s1 power drain and Teen Titans Cyborg regenerates health rapidly when tagged out. They do fairly little damage, however.
Chaos is frustrating as usual. Boss Solomon Grundy's passive allows his heavy combos to do almost 23000 damage at critical health, which is worsened by Green Lantern John Stewart's passive, which turns teammates invulnerable for 4 seconds upon falling below 20% health. Luchador Bane's ~70% chance of unblockable stun on tag in leads to a chance of him laying waste to your team with an unavoidable s2 that could potentially do almost 95000 damage. Green Lantern/Red Son may be helpful, as he provides himself, along with the other Red Son teammate you choose, with stun-immunity.
This battle is a fairly typical battle, but Containment Doomsday can be a pain in the neck. Specials that have multiple hits, like Cassandra Cain's No Man's Lan or Arkham Origins Deathstroke's Identity Crisis are very useful when battling him.
Challenge: Radiation! (You will lose 1% maximum health every second)
600 Wonder Woman and Animated Harley Quinn gives the whole team +50% power generation and damage. Not only they would get power to use specials incredibly quickly, Batman Returns Catwoman's s2 can do over 130,000 damage if Harley uses her team damage boost. Catwoman also boosts the bleeding damage on 600 WW's s2.
Challenge: Countdown! (You have 2 minutes to defeat your opponents)
Red Son Wonder Woman gives the entire team +45% power generation, Superman +75% basic damage, and Deathstroke +15% speed.
The first match in this battle to have a soup-up opponent with about twice the normal health. With his passive (+45% health to team), Red Son Solomon Grundy will have over 180,000 health, while Green Lantern causes the team to take -20% special and super damage and immune to stun and crit. Finally, Red Son Batman gives their special 1 a high chance of being unblockable.
Remember that power drain will still work despite Green Lantern's plethora of protections.
If you don't have Raven/Prime (who is also slightly less effective if you don't have her elited due to unblockable s1), Batgirl/Cassandra Cain is an excellent choice here, since she deals 25% current health damage whenever she tags in, ignoring their defences.
If you don't have her either, Black Adam/Regime is a decent choice, since his passive also reflects double s1 damage (also irreducible) and unblockable s1 is thus less of an issue to him, although his base stats are extremely low. Health gear is good for this purpose.
The Ibistick can be used to cause Red Son Solomon Grundy to burn for a total of up to 10% of his total health whenever you use a special.
Mostly a relatively harmless drag-fight due to the dampening field, Luthor's increased team health, as well as his and Nightwing's frequent power drains.
Ares' s2 can do over 80000 unblockable damage. Power drain should be used to handle him unless you could afford to sacrifice one of your characters. Cassandra Cain Batgirl causes you to lose 25% current health when she tags in. Using a special to knock out a character and force her to tag in during the special can negate that. If you tag in at the same time, the damage will be negated, but her next basic or special attack will be unblockable. Aquaman's s2 summons an Atlantean Hero to fight for him, who cannot use specials and has low health; he can be conveniently knocked out by Doomsday to gain an extra 50% max health back.
Challenge: Dampening Field!
The Radiation in this match is extremely strong, taking out all your health in a single minute by itself. The 41k damage on Godfall Superman's card is misleading; he actually has 54.3k damage, allowing him to hit up to 35000 with his Flying Punches.