This segues into "layout wars". I'd do it as:

if (
   condition &&
   condition &&
   condition
   )
   {
   ...
   }
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unless the conditions were long in which case I'd migrate (all) the &&s to the start of the lines in similar fashion to your sample.

However that only slightly impinges on the real problem that you mention: many indentation levels. That is something that I try hard to avoid. Often early exits from a block, using modifiers and using subs can clean up mega-nesting. If not, be very consistent in your chosen style of indentation because if you're not then things get very nasty very quickly!