That is a very tame definition of "generalist" you have there.

Here, let's propose some things I'd expect a generalist to be able to do:

IT
===========

- Provision wired networks for small businesses/homes/labs
- Do basic troubleshooting of printers and networked printing (and know when to throw in towel)
- Setup and debug towers and rack servers from parts
- Provision wireless networks using access points for small businesses/homes/labs
- Setup and debug mail clients
- Setup and debug file servers
- Setup and provision virtual machines with network access
- Setup and debug scripts for common administration tasks
- Setup and secure user accounts on remote systems with centralized management
- Setup disaster recovery systems and policies for above
- Write project plans and deliverables for doing above
- Write cost analyses and bills of materials for doing above
- Explain existing service providers and when they'd be preferable to doing things in-house

Web
============

- Write front-end JS, without frameworks, to do basic tasks
- Write single-page app with proper history integration
- Write front-end JS using AJAX endpoints
- Write functional JS where appropriate
- Write CSS
- Write CSS with less pain using LESS/SASS/Stylus/whatever
- Write CSS with rough idea of compatibility concerns
- Write HTML from scratch
- Write responsive web pages (and know when this is a fool's errand)
- Explain how HTTP works, what it gets wrong, and what alternatives exist
- Write JS using websockets
- Write JS using webworkers
- Write JS using canvas (2D or 3D)
- Provision a basic website using turnkey hosting ( Heroku, etc. )
- Provision a basic website using virtual hosting ( Linode, Digital Ocean, etc. )

Software engineering
=======================

- Write useful and succinct comments in code
- Write useful and succinct documentation for projects
- Provide useful root-cause analysis for production failures
- Provide reasonable estimates for project completion
- Provision and use a centralized version control system (CVS, SVN, etc.) and explain its uses
- Provision and use a decentralized version control system (git, mercurial, etc.) and explain its uses
- Write useful and approriate tests for code (TDD, BDD, library unit tests, whatever)
- Provision continuous integration services for an application

Systems
==============

- Explain how different data types can be represented in memory
- Explain how filesystems work
- Explain functions of a kernel
- Explain at least 2 approaches to operating systems design
- Explain basic architecture for at least 1 processor family, and be able to provide design considerations (MIPS, x86, x64, Itanium, ARM, SPARC, etc.)
- Write organized project in a systems language (assembly, C, C++, D, Rust, Go)
- Create build environment for native code projects
- Create makefiles (or platform's equivalent)
- Write in systems language: hash table, linked list, resizable array, binary tree
- Write networking code in a systems language supporting IPv4, IPv6, and which can support lookups by hostname
- Write UDP code with reliability mechanisms
- Write TCP client code, explain common mistakes
- Write multithreaded code, explain concurrency approaches
- Write asynchronous code in a systems language
- Write cross-language binding for systems language library ( Ruby over C, Python over C, etc.)
- Create and document binary format for storing structure data to a file
- Create and document binary format for streaming and message-based communication over a network
- Explain why we prefer JSON for above purposes
- Explain why JSON is slow and dumb, and we'd rather use <CapnProto, protocol buffers, STOMP, whatever > instead
- Write code handling file IO using normal methods, using asynchronous methods, using memory mapping in systems language
- Write code performing IPC in systems language

Databases
===============

- Provision an RDBMS (MariaDB, Postgres, whatever)
- Write basic queries for fetching data
- Write useful and succient data model documentation for database
- Explain performance considerations for hardware running that RDBMS
- Perform maintenance (backups, benchmarking) on RDBMS
- Provision at least one NoSQL solution (neo4j, MongoDB, Redis, Cassandra, etc.)
- Perform maintenance (backups, benchmarking) on NoSQL databases)
- Explain when to use that NoSQL solution in preference of an RDBMS, and why.
- Perform ETL using above systems
- Perform map-reduce using above systems
- Collect real-time time-series data using above systems
- Connect to above systems using web framework of choice, using manual and secure queries
- Connect to above systems using web framework of choice, using an ORM
- Scale database of choice across multiple machines
- Perform failover of database of choice across multiple machines

Maths
==============

- Understand basic linear algebra and rigid transforms (i.e., 2D graphics)
- Understand basic statistcal properties
- Understand basic themes of intergration and differentation
- Understand IEEE 754 floating-point and basic numerical issues in computation
- Understand trigonometric functions and their relations
- Estimate computational complexity of implementing above

This is not an exhaustive list, and I don't expect everyone to be 100% on it. That said, if you call yourself a "generalist" and can't do like at least half of everything in each of those categories, you're either a novice generalist, or you're full of shit.

EDIT:

I left out so things applying to programming languages, applying to machine learning, applying to graphics, applying to electronics, and several other things. Being a generalist is hard.

This is also why a good one is expensive.