Since the original discussion thread got deleted and people have been hijacking the loot thread to talk strategy, guess its time for another guide. this one will cover mainly level 5 and 6 since level 4 and below is pretty easy

Time Rift-Tidal Temple
Enemy Composition: Teams centered around the 3 Naga heros; Depth's Voice, Vengeance Spirit and Savage One
Suggested team: Tank + Death Mage + Frost Mage + Mystic + Chapplin/Commando/any DPS (Cloud Walker is the best)
Main Problem: Ensuring that your team can survive being chipped away by Vengeance Spirit's split shots and being hit by Ultis that freeze your team in place
Strategy: Your team will center around the damage capabilities of your 3 caster heroes, with your BEST tank leading the charge (Warchief or Drunken Master usually), the last spot is a bit tricky; try using Chapplin to see if she can get through the whole round without being killed, if not try Commando as her Agility bonus increases armour and helps to resist damage from enemy Vengeance Spirit.
MVP: Interestingly I found that the MVP is actually Mystic. His blind helps a lot and for some reason Vengeance Spirit's ulti always misses him (for me). I've breezed through even if my heroes are turned to stone by simply chipping the enemy away with a Death Mage ulti that was casted before hand and Mystic's Ulti.

Time Rift-Dwarf Arsenal
Enemy Composition: Highly durable frontline tanks protecting a soft backline, most of the enemies have AOE attacks.
Suggested team: Arcane Sapper + Death Mage + Chapplin + 2 other Tanks (generally any 2 Front Heros)
Main Problem: Ensuring that your team doesn't die and that they don't lose to timeout because you lack DPS
Strategy: I've had the most fun with this one trying out lineups and generally this is the easiest. Because of the high AOE damage it's usually not a good idea to use too many Back and Middle heroes (except Death Mage because of her crazy regen) and also to have more than 2 heroes per "zone".
MVP: Arcane Sapper. He'll teleport to the backline, solo against 3 enemies and not die because of dodge and lifesteal. Honorable mention to Death Knight because he simply wont die, but doesn't do a lot of damage so skipping him is no issue.

Trial- Crashed Hill
Enemy Composition: Sturdy, low damage frontline tanks protecting very squishy backlines. Most enemies have no AOE so there will be a lot of pressure on your tank.
Suggested team: Death Mage + Frost Mage + Mystic + Your best Tank + Any hero who can do good magic damage like Machinist(best choice!)/Succubus/Luna Guardian/Old Curse
Main Problem: Since your mages need to charge ultis, your tank needs to buy enough time.
Strategy: Use your best tank and see if he/she can survive at least till your mages can ulti. If he/she can't, use the last spot for a healer but watch to ensure you're doing enough damage. Death Mage can tank both melee enemies in stage 3 if your tank dies before then.
MVP: With Mystic and Frost Mage support, Death Mage does crazy AOE damage, kills enemy backline before they can do anything and heal herself and tank (generally what she does in Crusade)

Trial- Cursed City
Enemy Composition: Strong short-range frontliners protecting a single fragile Witch that has a polymorph spell and slow firing, extremely high damage, single target, shots.
Suggested team: Warchief + Shadowleaves + Cloud Walker/Fallen + Shadow Shaman (At lvl 69, his PS will allow your entire team to crit on every physical attack for level 5, not sure about level 6 but shouldn't be far off. Highly reccomended.) + Disease Bringer. You can also mix and match Fallen Dominion/Luna Guardian/Vengeance Spirit/Arcane Sapper in
Main Problem: Killing the witch before she gets a chance to assassinate your heroes 1 by 1.
Strategy: If you're using the recommended team, its a breeze watching the Witch hit your Cloud Walker Illusions and Hellfire Golem(s). If you are not using either but have Arcane Sapper, its a bit tricky as he will cause the Witch to flinch with almost every hit, but will likely die in one hit himself so you have to reset a few times and time his ulti properly to ensure that you do enough damage to the witch so someone else like Luna Guardian can finish her off.
MVP: Remember what I said about the Witch? Well Cloud Walker will summon clones that absorb her shots faster then she can shoot them and sometimes she'll even polymorph those clones! With Shadow Shaman's help, his ulti will do much much more damage as well as boosting his clone's normal damage.

Trial- Valkyrie
Enemy Composition:
Suggested team:
Main Problem:

TBC tomorrow (maybe) because it's late now