How to align the conditions in a hierarchical structure?

Here's a solution that uses the multirow package and its eponymous command \multirow:

\documentclass{article}
\usepackage{amsmath,multirow}
\begin{document}
\noindent
Original code:
\begin{equation*}
\text{Start} 
\left\{\begin{aligned} \text{Do A,} \quad \quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text{if a happens} \\
\text{otherwise} \left\{\begin{aligned} \text{Try B,}
    \quad \quad \quad \quad \quad \quad \quad\quad\quad \text{if b occurs}\\
\text{Try C} \left\{\begin{aligned} \text{Perform C1}  \quad \quad \text{if
      c increases}\\
\text{Perform C2, } \quad \text{if c decreases}
\end{aligned} \right.
\end{aligned} \right.
\end{aligned} \right.
\end{equation*}

\bigskip\noindent
New code:
\begin{equation*}
\text{Start}
\left\{ \begin{array}{ll}
   \text{Do A} & \text{if a happens}\\
   \multirow{3}{*}{$ % restart math mode
       \text{otherwise}  
       \left\{ \begin{array}{l}
         \text{Try B}\\
         \text{Try C} 
           \left\{ \begin{array}{l}
              \text{Perform C1}\\
              \text{Perform C2}
           \end{array} \right.
       \end{array} \right. %
   $} %  end of scope of multirow
   & \text{if b occurs   } \\
   & \text{if c increases} \\
   & \text{if c decreases} 
\end{array} \right.
\end{equation*}
\end{document}

Remark: This solution is similar in structure (and, in particular, the use of nested arrays) to the one provided in @Werner's answer to an earlier question, except that the multirow package is used to here to typeset correctly the otherwise string (and the subsequent material)

---

Addendum: The OP has asked how one would exchange the order of the TryB/TryC items. To do so, exchange the order of the two rows in the middle of three array structures and (ii) rearrange the order of the "if b occurs"/"if c increases"/"if c decreases" strings.

\documentclass{article}
\usepackage{amsmath,multirow}
\begin{document}
\begin{equation*}
\text{Start}
\left\{ \begin{array}{ll}
   \text{Do A} & \text{if a happens}\\
   \multirow{3}{*}{$ % restart math mode
       \text{otherwise}  
       \left\{ \begin{array}{l}
         \text{Try C} 
           \left\{ \begin{array}{l}
              \text{Perform C1}\\
              \text{Perform C2}
           \end{array} \right. \\
         \text{Try B}
       \end{array} \right. %
   $} %  end of scope of multirow
   & \text{if c increases} \\
   & \text{if c decreases} \\
   & \text{if b occurs} 
\end{array} \right.
\end{equation*}
\end{document}

You can change the interline spacing by resetting the length \LSG, currently set to 1.4\baselineskip. The rest just stacking, and scaling the braces to the stack height.

\documentclass{article}
\usepackage[usestackEOL]{stackengine}[2013-10-15]
\usepackage{scalerel}
\newcommand\rbsa[2]{\raisebox{#1}{\scaleleftright[2ex]{\{}{#2}{.}}}
\def\stacktype{L}
\def\stackalignment{l}
\newlength{\LSG}
\setlength{\LSG}{1.4\baselineskip}
\setstackgap{L}{\LSG}
\begin{document}
\savestack{\cstack}{\rbsa{.5\LSG}{\stackunder{Perform C1}{Perform C2,}}}
\savestack{\bcstack}{\rbsa{\LSG}{\stackunder[1.5\LSG]{Try B,}{Try C\cstack}}}
\savestack{\abcstack}{\rbsa{1.5\LSG}{\stackunder[2\LSG]{Do A}{otherwise\bcstack}}}
Start\abcstack~~~~~~\Centerstack[l]
{if a happens\\if b occurs\\if c increases\\if c decreases}
\end{document}

To get the alternate format, referenced by the OP:

\documentclass{article}
\usepackage[usestackEOL]{stackengine}[2013-10-15]
\usepackage{scalerel}
\newcommand\rbsa[2]{\raisebox{#1}{\scaleleftright[2ex]{\{}{#2}{.}}}
\def\stacktype{L}
\def\stackalignment{l}
\newlength{\LSG}
\setlength{\LSG}{1.4\baselineskip}
\setstackgap{L}{\LSG}
\begin{document}
\savestack{\cstack}{\rbsa{.5\LSG}{\stackunder{Perform C1}{Perform C2,}}}
\savestack{\bcstack}{\rbsa{0.5\LSG}{\stackunder[1.5\LSG]{Try C\cstack}{Try B,}}}
\savestack{\abcstack}{\rbsa{1.5\LSG}{\stackunder[2\LSG]{Do A}{otherwise\bcstack}}}
Start\abcstack~~~~~~\Centerstack[l]
{if a happens\\if c increases\\if c decreases\\if b occurs}
\end{document}

I find the given structure a little difficult to follow: some of the if conditions are much to far from the actions they govern. Also, it seems that there ought to be another "otherwise" just before "Try C". I would reorganize the whole thing:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\text{Start}
\ \begin{cases} \text{if a happens}& \text{Do A,} \\
                \text{otherwise}&
    \begin{cases}\text{if b occurs}& \text{Try B,}\\
                 \text{otherwise}& \text{Try C}
    \ \begin{cases}\text{if c increases}& \text{Perform C1,}\\
                   \text{if c decreases}& \text{Perform C2.}
      \end{cases}
    \end{cases}
  \end{cases}
\end{equation*}
\end{document}