Custom Navigation in Beamer Footer

So if I get you right, you basically want to change the drawing in the TikZ code. First of all we can simply, because the shapes do not differ based on the section. Then we adapt the drawing and the colors to follow your example. Basically the drawing happens in two steps. First fill an area that is to your liking fill[fill=blue,draw=none] (0,0) -| (1.5,0.2) -- (0.4,0.2) -- (0.3,0.3) -- (0.2,0.2) -| cycle;, then add a node below that contains the text node(text)[text=blue,anchor=north west] at (0,0) {strutinsertsectionheadhskip.3cm};

documentclass{beamer}

usepackage{tikz}
usetikzlibrary{shapes,calc,positioning,arrows}
setbeamertemplate{navigation symbols}{}
setbeamertemplate{footline}{%
leavevmode%
  hbox{%
    begin{beamercolorbox}[wd=paperwidth,ht=4.8ex,dp=5.125ex]{palette}%
        insertsectionnavigationhorizontal{paperwidth}{}{hskip0pt plus1filll}
    end{beamercolorbox}%
  }
}

setbeamertemplate{section in head/foot}{%
begin{tikzpicture}%
    node[anchor=north west,inner sep=0pt,outer sep=0pt,text=white] at (0,0.3) {hyperlink{Outlineinsertpartheadnumber.insertsectionheadnumber}{rule{1.5cm}{0.6cm}}};
    fill[fill=blue,draw=none] (0,0) -| (1.5,0.2) -- (0.4,0.2) -- (0.3,0.3) -- (0.2,0.2) -| cycle;
    node(text)[text=blue,anchor=north west] at (0,0) {strutinsertsectionheadhskip.3cm};
end{tikzpicture}
}

setbeamertemplate{section in head/foot shaded}{%
begin{tikzpicture}%
        node[anchor=north west,inner sep=0pt,outer sep=0pt,text=white] at (0,0.3) {hyperlink{Outlineinsertpartheadnumber.insertsectionheadnumber}{rule{1.5cm}{0.6cm}}};
        fill[fill=blue!50,draw=none] (0,0) -| (1.5,0.2) -| cycle;
        node(text)[text=blue,anchor=north west] at (0,0) {strut};
end{tikzpicture}
}

begin{document}

section{objective 1}
begin{frame} frametitle{My First Slide} Slide 1 end{frame} 

section{objective 2}
begin{frame} frametitle{My Second Slide} Slide 2 end{frame} 

section{objective 3}
begin{frame} frametitle{My Second Slide} Slide 2 end{frame} 

end{document}

---

Addition to your request to have a working link

Actually beamer uses targets that are named Outline<part>.<section> to identify the starting page of a section. beamer also offers the hyperlink command to link to such targets. A quick&dirty solution I found is to put a surface in the background that can be used for the link and then refer to the section by using the given part and section number. Therefore we are adding this line: node[anchor=north west,inner sep=0pt,outer sep=0pt,text=white] at (0,0.3) {hyperlink{Outlineinsertpartheadnumber.insertsectionheadnumber}{rule{1.5cm}{0.6cm}}};

I am sure there is a better solution to create an empty box in the node for the hyperlink to work, in this case you could remove the text=white and maybe also dynamically adjust the size of the node to the actual content. Nevertheless this solution produces a link for the area of the rectangle and button, if you want to see the size, change text=white to text=red and it will be drawn red.