You can turn Life into Shit in 6 steps:
LIFE → LIFT → LOFT → LOOT → SOOT → SHOT → SHIT
LIFE → LIFT → SIFT → SOFT → SOOT → SHOT → SHIT
LIFE → LIFT → LOFT → SOFT → SOOT → SHOT → SHIT
This is the optimal solution.
Why 6 steps?
Having 4 steps (the practical optimal solution) is not possible. Why? We need to change one letter at a time, and it is impossible:
Life- Sife? Lhfe? Liie? Lift
But when what do we go after LIFT? The only other option is SIFT, but what can we go after that? siit or shft? None, so therefore 4 steps won't work. 5 steps also wont work, so the only other option is the 6 steps, which is the answer.
My thinking solution:
After verifying that LIFE must go to LIFT, we have 3 options in front of us, as we have LOFT and SIFT. SIFT only goes to SOFT, and LOFT can go to SOFT OR LOOT, which then goes to the same thing: SOOT. From there, we can easily finish it off: SHOT and SHIT.