Joachim came through the youth system at Leicester City, and went on to score the club's first ever Premier League goal on the opening day of the 1994–95 season in a 3–1 home defeat to Newcastle United.

[3] He was cup-tied for their victory in the 1996 Football League Cup final having played in the competition for Leicester City earlier that season.

In 2004 Joachim moved to Leeds United, a club heavily in debt and in the process of rebuilding an inexpensive team, on a free transfer.

He made 10 starts and 17 substitute appearances in the league for Leeds that year, but could only deliver two goals before being loaned out to Walsall for the final two months of the season.

[9] He subsequently moved into non-league football, signing with newly promoted Conference North side King's Lynn in June 2008.

He briefly played as an amateur in the Leicestershire Senior League for Thurmaston Town at the start of the 2009–10 season, but a couple of weeks later he signed semi professional terms with Quorn.

[20] In the 2015–16 season Joachim played for Holwell Sports in the East Midlands Counties League, scoring ten goals in 36 appearances in all competitions.

[25] On 5 July 2018 Joachim signed for Nottinghamshire Senior League side Aslockton & Orston,[26] scoring 33 goals in 39 appearances in all competitions.