I will be telling you my experience with a successful trials run. I know that opinions may vary but I find it easiest to do archer class.
First go on top of the cauldrons at the start of the arena for the first 3 waves. Keep in mind that some mobs may not come to you immediately but that's okay because you can still aggro them later. One thing to keep in mind that is annoying to me is that baby zombies can fit under one block gaps so they may go under the cauldrons. On wave three I would recommend sniping the wither skeletons without them aggroing on you. Sometimes one may be in a position requiring you to get close to them but remember to keep backing up if they aggro on you.
On wave 4 I would recommend taking out the shulkers first as they can be really annoying because they can cause levitation on both you and the magma cubes and magma cubes don't take fall damage. Levitation also makes it harder for them to be killed as you have to lead in your bow shots more. Once the large magma cubes and medium magma cubes are killed it's time to switch to your sword as you can kill the small magma cubes in one hit and they are not dangerous.
Before the next wave starts (I suggest leaving one magma cube alive for this) you should have between 40 to 60 levels from killing all the mobs. Buy the iron armor (not the sword) and if you have excess level buy 2 fire res potions and one speed potion. and spend the rest on gapples and an ender pearl.
On wave 5 be ready for all hell to break loose as you are bombarded with strays, husks, and polar bears. Just flank the husks and polar bears by using the outer rim as a lead in for your shots, and kill the strays by staying away from them. (remember you have better aim then skeletons or strays) Sometimes strays will shoot the husks or polar bears making it easier to kill them. Sometimes a polar bear or two will remain for the next wave so try to kill them first.
Wave six consists of endermen and witches. Use the cauldron technique for the endermen and shoot the witches from away so that they can't poison or slow you. Leave one alive to buy any last minute stuff then kill it from closer than the other two. (this is important for the next wave)
wave 7 is evokers one or two will spawn next to you depending on which witch you left alive. Shoot the one or ones closest to you immediately so that you have less to worry about. By this time vexes have spawned in from the evokers and you need to get a lead on them. Don't fight the vexes that will only get you killed. once all the evokers are dead run from the vexes and if you are feeling brave shoot a couple and they will die after a short time.
wave 8 is blazes and vindicators. Kill the blazes first by shooting them. (don't worry about fire res the fire won't last long if you get hit and you will need it later) Then kill the vindicators without getting in range of their iron axes and leave one alive in the outer ring so you can start next wave in safety.
wave 9 (you are almost there) has iron golems, ghasts, and more blazes. You need to take out the blazes first again but you might spawn with an angry iron golem near you. In that case, back away into the outer ring and slowly whittle down it's health. Some ghasts will annoy you but their fireballs are relatively slow and give you plenty of time to move out of the way. They are also hard to reach though but with a fully charged bow shot will only take one hit to kill. Leave one iron golem alive to prepare for the boss and kill it in the outer ring.
Boss Wave. You made it. All that hard work will finally pay off. If you beat the boss. Zulrah will change states periodically from his normal wielding a blaze rod, to his fire breath holding blaze powder, ice breath which will slow you if you get hit but can be dodged and wielding a snowball, his attack form where he can charge at you causing nausea and throwing you in the air or body slam you causing slowness and he wields two diamond swords, and his wither form where he shoots three wither skulls at a time and getting hit by one of those or even being near him for too long will wither you for a few seconds and he wields two diamond hoes. Just lead him through the outer ring while shooting him, eating gapples and drinking potions as necessary (I recommend drinking the speed potion at the start of the fight as he is quick) and near the end of the fight ender pearl away to deal the final few hits on him. Congratulations you have completed the ancient trials.
A final tip is to eat your gapple before the start of the trials as you keep the absorption and the gapple is still in your inventory when wave one starts.
First go on top of the cauldrons at the start of the arena for the first 3 waves. Keep in mind that some mobs may not come to you immediately but that's okay because you can still aggro them later. One thing to keep in mind that is annoying to me is that baby zombies can fit under one block gaps so they may go under the cauldrons. On wave three I would recommend sniping the wither skeletons without them aggroing on you. Sometimes one may be in a position requiring you to get close to them but remember to keep backing up if they aggro on you.
On wave 4 I would recommend taking out the shulkers first as they can be really annoying because they can cause levitation on both you and the magma cubes and magma cubes don't take fall damage. Levitation also makes it harder for them to be killed as you have to lead in your bow shots more. Once the large magma cubes and medium magma cubes are killed it's time to switch to your sword as you can kill the small magma cubes in one hit and they are not dangerous.
Before the next wave starts (I suggest leaving one magma cube alive for this) you should have between 40 to 60 levels from killing all the mobs. Buy the iron armor (not the sword) and if you have excess level buy 2 fire res potions and one speed potion. and spend the rest on gapples and an ender pearl.
On wave 5 be ready for all hell to break loose as you are bombarded with strays, husks, and polar bears. Just flank the husks and polar bears by using the outer rim as a lead in for your shots, and kill the strays by staying away from them. (remember you have better aim then skeletons or strays) Sometimes strays will shoot the husks or polar bears making it easier to kill them. Sometimes a polar bear or two will remain for the next wave so try to kill them first.
Wave six consists of endermen and witches. Use the cauldron technique for the endermen and shoot the witches from away so that they can't poison or slow you. Leave one alive to buy any last minute stuff then kill it from closer than the other two. (this is important for the next wave)
wave 7 is evokers one or two will spawn next to you depending on which witch you left alive. Shoot the one or ones closest to you immediately so that you have less to worry about. By this time vexes have spawned in from the evokers and you need to get a lead on them. Don't fight the vexes that will only get you killed. once all the evokers are dead run from the vexes and if you are feeling brave shoot a couple and they will die after a short time.
wave 8 is blazes and vindicators. Kill the blazes first by shooting them. (don't worry about fire res the fire won't last long if you get hit and you will need it later) Then kill the vindicators without getting in range of their iron axes and leave one alive in the outer ring so you can start next wave in safety.
wave 9 (you are almost there) has iron golems, ghasts, and more blazes. You need to take out the blazes first again but you might spawn with an angry iron golem near you. In that case, back away into the outer ring and slowly whittle down it's health. Some ghasts will annoy you but their fireballs are relatively slow and give you plenty of time to move out of the way. They are also hard to reach though but with a fully charged bow shot will only take one hit to kill. Leave one iron golem alive to prepare for the boss and kill it in the outer ring.
Boss Wave. You made it. All that hard work will finally pay off. If you beat the boss. Zulrah will change states periodically from his normal wielding a blaze rod, to his fire breath holding blaze powder, ice breath which will slow you if you get hit but can be dodged and wielding a snowball, his attack form where he can charge at you causing nausea and throwing you in the air or body slam you causing slowness and he wields two diamond swords, and his wither form where he shoots three wither skulls at a time and getting hit by one of those or even being near him for too long will wither you for a few seconds and he wields two diamond hoes. Just lead him through the outer ring while shooting him, eating gapples and drinking potions as necessary (I recommend drinking the speed potion at the start of the fight as he is quick) and near the end of the fight ender pearl away to deal the final few hits on him. Congratulations you have completed the ancient trials.
A final tip is to eat your gapple before the start of the trials as you keep the absorption and the gapple is still in your inventory when wave one starts.