たちまち・いきなり: the difference
たちまちN2
Meaning
Immediately, Quickly, Suddenly, In a moment or flash
Past papers
Example
少し油断したら、ライバルに忽ち追い越された。
(I) was only slightly negligent, but (my) rival immediately overtook me.
いきなりN2
Meaning
For no reason, Suddenly, All of a sudden
Past papers
Example
行き成りの展開に驚きを隠せない。
I can't hide my surprise at the sudden development.
How to tell them apart
「たちまち」: stresses how fast a big change happens; you marvel at it afterwards.
「すぐに」: just a short gap between two things; works for your own actions: 「すぐ行きます」.
「いきなり」: stresses no warning, abrupt, unexpected.