"Is there any way for a cleric to actualy play solo, and if there is how to do it?"
My answer is: depends
Depends of your level, depends of what you want to do, depends of your gear and depends of the pets you have.
If your intention is to grab skill points, well, you have no option, you HAVE to solo (mainly because nobody lately on LC wants to make party with a "leeching" cleric stealing skill points. Unfortunately is now a solo game, but let's see how it will be in some days...
If your intention is to power level I would say that depends. If you have A LOT of pots and equip +15 and with a good pet you can. It will take a lot of time to you kill, but it is not impossible. Of course it is MUCH better with a party (much faster too). also depends of the level of the monster and your own. If you are a cleric 59 DO NOT TRY to solo a demon, you can't. Well, in fact you can, but will take around 10 minutes to you solo one, so in the end it won't worth. If you are 88 with at least +13 armor and +15 weapon you can solo a zombie or a fighter or even a spearman on tomb. If you are a cleric 115 you also can't solo a sorcerer on Spirit's cave, except if you bought the whole item mall of potions and medicines.
I know my reply was kinda vague, maybe if you say your level and what you want to do right now might help?
I also did a "mini guide" once in a topic, maybe your question may be cleared there:
If I still didn't reply to you, just shout!