Okay, after putting a lot of hours into this, I'm getting close to finishing the SP trials. I've been compiling this information as I've played through it, and as said in other solutions, making a guide for each trial isn't feasable. I just thought I'd try to add to your knowledge with some little tricks to help you get through these trials. If there's anything I've missed, or any information you can add to make this a better guide, please leave a comment, and I'll credit you for it.
These trials are very difficult, and half of the battle is picking yourself up mentally after the first few losses, because it seems like some trials are impossible after the first few tries. Keep plugging away though, and you will get your rewards.
Lesser Minions and Babies can be taken out with a simple grab (RT) and punish. This is very useful for "Take No Damage" and "Don't Kill the Prisoner" trials.
A lot can be said for the simple double jump, then spam B combo with Dante. Keep on the move while doing this. It keeps you out of the way of ranged attacks, while dealing a fair amount of damage. With Lucia, just fly around on the floor weaving, and using the hold B attack.
Use your magic wisely, I cannot stress this enough. The only magic I used was Divine Armour. It helps a LOT with the "Take No Damage" trials, and when you have to face multiple large enemies. Keep an eye on your magic meter, if you can, save magic to use in the later waves. If your health dips below 1/2, then use Divine Armour to bring it back up and give you a much needed breather.
On "Marked for Death" trials, try to run towards the enemy which is marked for death as soon as you can, then spam quick attacks before the others gather around you. You can get a great headstart this way. Lucia's hold B attack works wonders if you can get your aiming right.
On "Don't Kill the Prisoner" trials, just run away from the crowd, the prisoner runs faster than most other enemies, then double jump over the prisoner and spam B for Dante, hold B for Lucia. Again, this works wonders and if you get the aiming right, you won't hit the prisoner. When Lesser Minions and Babies are involved, don't forget to grab and punish them.
After the training trials, start off playing Path to Enlightenment, then move on to Gates of Hell 2. These are great practice maps which give a variety of situations, which can also build your confidence.
Some maps are easy to fall from, so watch out. You can use this to your advantage however. Spinning Minions can be thrown off the map sometimes. Also, spamming B makes the Demons fall back, very often they can fall off the edge, saving you time and health.
The order I tend to kill enemies is as follows, however depending on how you play, you may kill in a different order. Summoners are always first though, as you cannot kill the others without taking him out.
Summoners >> Heretics >> Pests and Minions >> Exploding, etc. Minions >> Greater Demons >> Spinning Minions >> Malecoda's.
The reason I kill in this order, rather than taking out the main threats first, is that after taking out the Summoners and Heretics, I spam B at the Pests and Minions, taking them out quickly, meaning less enemies are aiming at me. I can then focus on the main threats afterwards. I leave the Spinning Minions to the end because they sometimes hit other enemies, helping you. They're also hard to take down while other enemies are after you.
Methods for killing various enemies:
Minions (Weakest human-like enemies) - Fast attacks work best, either simply hit them with the cross, or use the combo hold LT and hit B three times. Another good way to kill these is to just grab (RT) them, and punish them. Use the first method in "Kill 'em Quick" trials though.
Pests (Flying bat-like enemies) - Cross works best on these. With Lucia, hold B then release for a quick way to kill them.
"A much quicker way of getting rid of pests (the flying bug looking things) is to jump in the air and hit RT. You will grab them and slam them to the ground with an instant kill. I've tested it on all versions of the pests, all medals, all difficulty, and even when magic protected. Instant kill each time." ~ Thanks, Draco719.
Spinning Minions - Righteous Path stops these guys from spinning, but this uses valuable magic. I find the best way is to either let them spin until they stop by holding block, or if you can block just as they hit you, it strikes them, which stops the spinning. When you get them to stop, a quick way to kill with Dante is to hold LT and spam Y.
Fire Minions, Smoke Minions, Exploding Minions - These are simple to kill, just hit them with the cross, then use X to swipe around you for a certain hit.
Lust Demons, Gluttons, Templars (Soldiers) - The best way I found to deal with these is to keep as far away as possible and spam B. Just keep hitting them, they will fall eventually, and it's a lot safer than going up close.
Greater Demons, Flying Demons, Malecoda - Keep as far away as possible from these, they will kill you FAST, especially if they're not alone. Keep away and again, spam B with Dante, hold B with Lucia. Punish them as soon as you can. With the flying demons, another guide said to forget about cutting off the wings. I strongly advise against this, taking their wings off gives them one less way of killing you, and that flying attack is the hardest to dodge. Malecoda's are tough, the safest way to take them out is to hit them with the cross until they turn black, then try to hit them a few times with Y,Y,Y,Y combos. When they stamp on the floor, double jump, or you won't last very long.
Heretics (Spellcasters) - The best way to deal with these is to use Divine Armour, and then spam Y,Y,Y,Y at them. It disposes of them quickly so you can then use the cross on other enemies. Keep double-jumping to avoid the spells, and block if they get close. These guys can really hurt you.
"For Heretics use LT+A , it will send them into the air allowing you to juggle them with x, netting you 7-8 free hits. Once they get up, repeat if they didn't die the first time." ~ Thanks, Anaxaminder.
Summoners - Trials with a summoner seem difficult, but they aren't when you know which tactic suits you best. What I did was ignore everything else on the map, running side to side and using Y,Y on the summoner, which would hit him twice before he vanished.