#JavaScript (ES6), 174 bytes

###Commented

JavaScript (ES6), 174 bytes

Commented

#JavaScript (ES6), 175 bytes

p=>a=>(r=F=([x,y],n,R=a[y],c=R[x])=>R[c==(R[x]=4)|n>=r||[-1,0,1,2].map(d=>(g=_=>(k=a[v=Y,Y+=d%2][h=X,X+=~-d%2])||g())(X=x,Y=y)>3?0:k>2?r=-~n:F(k>1?[X,Y]:[h,v],-~n)),x]=c)(p)|r 

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p => a => ( // given the starting position p[] and the matrix a[] r = // r = best result, initialized to a non-numeric value F = ( // F = recursive function taking: [x, y], // (x, y) = current position n, // n = number of shots, initially undefined R = a[y], // R = current row in the matrix c = R[x] // c = value of the current cell ) => // R[ // this will update R[x] once the inner code is executed c == (R[x] = 4) | // set the current cell to 4 (water); abort if it was n >= r || // already set to 4 or n is greater than or equal to r [-1, 0, 1, 2].map(d => // otherwise, for each direction d: (g = _ => ( // g = recursive function performing the shot by k = a[ // saving a backup (h, v) of (X, Y) v = Y, Y += d % 2][ // and updating (X, Y) until we reach a cell h = X, X += ~-d % 2]) // whose value k is not ice (k != 0) || g() // )(X = x, Y = y) // initial call to g() with (X, Y) = (x, y) > 3 ? // if k = 4 (water -> fail): 0 // abort immediately : // else: k > 2 ? // if k = 3 (hole -> success): r = -~n // set r to n + 1 : // else: F( // do a recursive call to F(): k > 1 ? // if k = 2 (sand): [X, Y] // start the next shots from the last cell : // else (wall): [h, v], // start from the last ice cell -~n // increment the number of shots ) // end of recursive call ), x // end of map(); x = actual index used to access R[] ] = c // restore the value of the current cell to c )(p) | r // initial call to F() at the starting position; return r 

#JavaScript (ES6), 174 bytes

p=>a=>(r=F=([x,y],n,R=a[y],c=R[x])=>R[c&(R[x]=4)|n>=r||[-1,0,1,2].map(d=>(g=_=>(k=a[v=Y,Y+=d%2][h=X,X+=~-d%2])||g())(X=x,Y=y)>3?0:k>2?r=-~n:F(k>1?[X,Y]:[h,v],-~n)),x]=c)(p)|r 

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p => a => ( // given the starting position p[] and the matrix a[] r = // r = best result, initialized to a non-numeric value F = ( // F = recursive function taking: [x, y], // (x, y) = current position n, // n = number of shots, initially undefined R = a[y], // R = current row in the matrix c = R[x] // c = value of the current cell ) => // R[ // this will update R[x] once the inner code is executed c & (R[x] = 4) |  // set the current cell to 4 (water); abort if it was n >= r || // already set to 4 or n is greater than or equal to r [-1, 0, 1, 2].map(d => // otherwise, for each direction d: (g = _ => ( // g = recursive function performing the shot by k = a[ // saving a backup (h, v) of (X, Y) v = Y, Y += d % 2][ // and updating (X, Y) until we reach a cell h = X, X += ~-d % 2]) // whose value k is not 0 (ice) || g() // )(X = x, Y = y) // initial call to g() with (X, Y) = (x, y) > 3 ? // if k = 4 (water -> fail): 0 // abort immediately : // else: k > 2 ? // if k = 3 (hole -> success): r = -~n // set r to n + 1 : // else: F( // do a recursive call to F(): k > 1 ? // if k = 2 (sand): [X, Y] // start the next shots from the last cell : // else (wall): [h, v], // start from the last ice cell -~n // increment the number of shots ) // end of recursive call ), x // end of map(); x = actual index used to access R[] ] = c // restore the value of the current cell to c )(p) | r // initial call to F() at the starting position; return r 

#JavaScript (ES6), 176 bytes

p=>a=>(r=F=([x,y],n,R=a[y],c=R[x])=>R[c<(R[x]=4)&&[-1,0,1,2].map(d=>(g=_=>(k=a[v=Y,Y+=d%2][h=X,X+=~-d%2])||g())(X=x,Y=y)>3?0:k>2?r=n>=r?r:-~n:F(k>1?[X,Y]:[h,v],-~n)),x]=c)(p)|r 

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p => a => ( // given the starting position p[] and the matrix a[] r = // r = best result, initialized to a non-numeric value F = ( // F = recursive function taking: [x, y], // (x, y) = current position n, // n = number of shots R = a[y], // R = current row in the matrix c = R[x] // c = value of the current cell ) => // R[ // this will update R[x] once the inner code is executed c < (R[x] = 4) && // set the current cell to water; if it was not already [-1, 0, 1, 2].map(d => // set to water, then for each direction d: (g = _ => ( // g = recursive function performing the shot by k = a[ // saving a backup (h, v) of (X, Y) v = Y, Y += d % 2][ // and updating (X, Y) until we reach a cell h = X, X += ~-d % 2]) // whose value k is not ice (k != 0) || g() // )(X = x, Y = y) // initial call to g() with (X, Y) = (x, y) > 3 ? // if k = 4 (water): 0 // abort immediately : // else: k > 2 ? // if k = 3 (hole): r = n >= r ? r : -~n // if n is less than r, then set r to n+1 : // else: F( // do a recursive call to F(): k > 1 ? // if k = 2 (sand): [X, Y] // start the next shots from the last cell : // else (wall): [h, v], // start from the last ice cell -~n // increment the number of shots ) // end of recursive call ), x // end of map(); x = actual index used to access R[] ] = c // restore the value of the current cell to c )(p) | r // initial call to F() at the starting position; return r 

#JavaScript (ES6), 175 bytes

p=>a=>(r=F=([x,y],n,R=a[y],c=R[x])=>R[c==(R[x]=4)|n>=r||[-1,0,1,2].map(d=>(g=_=>(k=a[v=Y,Y+=d%2][h=X,X+=~-d%2])||g())(X=x,Y=y)>3?0:k>2?r=-~n:F(k>1?[X,Y]:[h,v],-~n)),x]=c)(p)|r 

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p => a => ( // given the starting position p[] and the matrix a[] r = // r = best result, initialized to a non-numeric value F = ( // F = recursive function taking: [x, y], // (x, y) = current position n, // n = number of shots, initially undefined R = a[y], // R = current row in the matrix c = R[x] // c = value of the current cell ) => // R[ // this will update R[x] once the inner code is executed c == (R[x] = 4) | // set the current cell to 4 (water); abort if it was    n >= r ||  // already set to 4 or n is greater than or equal to r [-1, 0, 1, 2].map(d => // otherwise, for each direction d: (g = _ => ( // g = recursive function performing the shot by k = a[ // saving a backup (h, v) of (X, Y) v = Y, Y += d % 2][ // and updating (X, Y) until we reach a cell h = X, X += ~-d % 2]) // whose value k is not ice (k != 0) || g() // )(X = x, Y = y) // initial call to g() with (X, Y) = (x, y) > 3 ? // if k = 4 (water -> fail): 0 // abort immediately : // else: k > 2 ? // if k = 3 (hole -> success): r = -~n // set r to n + 1 : // else: F( // do a recursive call to F(): k > 1 ? // if k = 2 (sand): [X, Y] // start the next shots from the last cell : // else (wall): [h, v], // start from the last ice cell -~n // increment the number of shots ) // end of recursive call ), x // end of map(); x = actual index used to access R[] ] = c // restore the value of the current cell to c )(p) | r // initial call to F() at the starting position; return r