In the upcoming 5G-and-beyond era, ultra-reliable low-latency communication (URLLC) services will be ubiquitous in edge networks. To improve network performance and quality of service (QoS), URLLC services could be delivered via a sequence of software-based network functions, also known as service function chains (SFCs). Towards reliable SFC delivery, it is imperative to incorporate deterministic fault tolerance during SFC deployment. However, deploying an SFC with deterministic fault tolerance is challenging because the protection mechanism needs to consider protection against physical/virtual network failures and hardware/software failures jointly. Against multiple and diverse failures, this work investigates how to effectively deliver an SFC in optical edge networks with deterministic fault tolerance while minimizing wavelength resource consumption. We introduce a protection augmented graph, called k-connected service function slices layered graph (KC-SLG), protecting against k-1 fiber link failures and k-1 server failures. We formulate a novel problem called deterministic-fault-tolerant SFC embedding and propose an effective algorithm, called most candidate first SF slices layered graph embedding (MCF-SE). MCF-SE employs two proposed techniques: k-connected network slicing (KC-NS) and k-connected function slicing (KC-FS). Through thorough mathematical proof, we show that KC-NS is 2-approximate. For KC-FS, we demonstrate that k = 3 provides the best cost-efficiency. Our experimental results also show that the proposed MCF-SE achieves deterministic-fault-tolerant service delivery and performs better than the schemes directly extended from existing work regarding survivability and average cost-efficiency.