This is a specialist style, not a generalist one
Anime tattooing is built on things most tattooers never practise: razor-consistent linework, cel-shading, and colour packed saturated enough to read like a frame of animation. A brilliant all-rounder can still botch an anime piece, and most of the 'tattoo fails' content you've seen is exactly that: a generalist taking on a style they don't do. The fix is boring and reliable: only book artists whose portfolios are full of anime work, not one lucky piece.
It also helps to know which sub-style you're actually asking for, because they're different skill sets. Cel-shaded colour characters, black and grey manga panels with their screentone-style shading, and American 'new school' cartoon work with its exaggerated proportions are three different crafts. Look through your saved references and work out which one keeps showing up, then find the artist who lives in that lane. Browsing artists by style on REAP's discover pages is the fast way to see who near you actually specialises.
Manga panel, colour character, or symbol
The three standard formats, with honest trade-offs. Manga panels: black and grey, rectangular frames, usually forearms. They rely on contrast rather than colour so they age the most consistently, but the fine screentone shading needs negative space or it blurs; a good artist will adapt the panel for skin rather than copy it line for line. Colour characters: the highest impact and the highest maintenance. Bright pigments, especially pinks, yellows and light blues, fade fastest, and touch-ups every few years are normal for heavily saturated work, not a sign of failure.