The solution isn't to pay for shards, though that would speed up the process. Doomtower is end game content, it's supposed to be hard. At 115 you can't expect to be able to beat every part of the game. 

Continue playing as you have, build up your teams and collect your champions the same way you have been doing. Shield champions are pretty important in every aspect of the game and not just one boss in Doom tower. 

You're complete misunderstand what I am trying to say : it is NO FUN getting to lvl 89 one week and not getting past lvl 19 the next... end game content or not

how do you arouse old memories of a few days :)), you don't have heroes, you can't beat DT, but where are the heroes if you don't have shards? :) you still need a blunder like that a few days ago :)) 

Actually you should not expect to beat endgame content with an early account. After 115 days you should perhaps have other strategies. 

Metalshaper for example would also be a solution. 

At the moment I do not know what you do expect? There are rotations and the current on is the most difficult of all DT rotations. It is quite natural that you won't beat every rotation. 

And Scarab king is one of the oldest DT bosses....to which level do you get in the first rotation (the most easy one) in which Scarab is also present?

Although specific champions can make DT easier it is more about gear , if you shared your team builds we might be able to pinpoint the issue.

Here is a list of champs that give shield to your team. The combination of Valerie (campaign farmable, act 1) and Hungerer (uncommen) should be able to keep the shield up the whole fight. Lvl 40 is enough, they are just supposed to give the shield.

2x Armiger (one very fast and A1 only, second with some damage and destroy gear), Ma'Shalled should be good enough to do the stage once. Probably not your farming spot for materials in DT.

Who else are you using in your team? You're talking about Hard mode right?

Shield Rings .........

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As I said paying will speed up the process, but you don't have too. You earn shards by playing the game, i.e. dungeons, completing campaign, events etc. Thank you for asking, I hope this helps.  

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account f2p 

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account in which I invested money, and not a little 

Look at all those champs. Tons of stuff. Lots of quality 60s on both accounts.

I see the difference, yes. But even your F2P account is pretty strong, and could field some strong teams.

I would argue that not only have you spent money on your main account, it is also your MAIN account. You play it significantly more than your F2P, yes? If like people in my cluster, they play their second accounts maybe 5-10x less than their main accounts.